# Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns

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## Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns

The students who are lagging in the Factors, Multiples, and Patterns can learn through our Go Math Answer Key. Just tap the link and start preparing now. Refer Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns to enhance your skills and score well in the exams.

Lesson: 1 – Model Factors

Lesson: 2

Lesson: 3 – Problem Solving Common Factors

Lesson: 4 – Factors and Multiples

Lesson: 5 – Prime and Composite Numbers

Lesson: 6 – Number Patterns

Lesson: 7

### Common Core – Factors, Multiples, and Patterns – Page No. 97

Model Factors

Use tiles to find all the factors of the product.

Record the arrays on grid paper and write the factors shown.

Question 1. Question 2.
Write the factors of: 30
Type below:
_________

Answer: The Factors of 30 are: 1,2,3,5,6,10,15,30.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 30 when multiplied together.
1 × 30 =30
2 × 15 = 30
3 × 10 = 30
5 × 6 = 30
6 × 5 = 30
10 × 3 = 30
15 × 2 = 30
30 × 1 = 30
So the factors of 30 are 1,2,3.5,6,10,15,30.

Question 3.
Write the factors of: 45
Type below:
_________

Answer: The Factors of 45 are:1,3,5,9,15,45

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 45 when multiplied together.
1×45=45
3×15=45
5×9=45
9×5=45
15×3=45
45×1=45
So the factors of 45 are: 1,3,5,9,15,45.

Question 4.
Write the factors of: 19
Type below:
_________

Answer: The Factors of 19 are: 1,19

Explanation:
Since 19 is a Prime number that means it is divisible by 1 and itself.
1 × 19 = 19
19 × 1 = 19
So the factors of 19 are 1,19.

Question 5.
Write the factors of: 40
Type below:
_________

The Factors of 40 are:1,2,4,5,8,10,20,40.

Explanation:
Factors are the numbers that divide the original number completely.
1×40=40
2×20=40
4×10=40
5×8=40
8×5=40
10×4=40
20×2=40
40×1=40
The Factors of 40 are: 1,2,4,5,8,10,20,40.

Question 6.
Write the factors of: 36
Type below:
_________

Answer: The Factors Of 36 are:1,2,3,4,6,9,12,18,36.

Explanation:
Factors are the numbers which divides the original number completely.
1×36=36
2×18=36
3×12=36
4×9=36
6×6=36
9×4=36
12×3=36
18×3=36
36×1=36.
The factors of 36 are:1,2,3,4,6,9,12,18,36

Question 7.
Write the factors of: 22
Type below:
_________

Answer: The Factors Of 22 are:1,2,11,22.

Explanation:
Factors are the numbers that divide the original number completely.
1×22=22
2×11=22
11×2=22
22×1=22.
The factors of 22 are:1,2,11,22.

Question 8.
Write the factors of: 4
Type below:
_________

Answer: The Factors Of 4 are: 1,2,4.

Explanation:
Factors are the numbers that divide the original number completely.
1×4=4
2×2=4
4×1=4.
The Factors Of 4 are 1,2,4.

Question 9.
Write the factors of: 26
Type below:
_________

Answer: The Factors Of 26 are:1,2,13,26.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 26 when multiplied together.
1×26=26
2×13=26
13×2=26
26×1=26.
So the factors of 26 are:1,2,13,26.

Question 10.
Write the factors of: 49
Type below:
_________

Answer: The Factors Of 49 are: 1,7,49.

Explanation:
Factors are the numbers that divide the original number completely.
1×49=49
7×7=49
49×1=49.
The Factors Of 49 are 1,7,49.

Question 11.
Write the factors of: 32
Type below:
_________

Answer: The Factors Of 32 are:1,2,4,8,16,32.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 32 when multiplied together.
1×32=32
2×16=32
4×8=32
8×4=32
16×2=32
32×1=32.
So the factors of 32 are:1,2,4,8,16,32.

Question 12.
Write the factors of: 23
Type below:
_________

Answer: The Factors Of 23 are: 1,23.

Explanation:
Since 23 is a Prime number that means it is divisible by 1 and itself.
1×23=23
23×1=23.
So the factors of 23 are 1,23.

Question 13.
Brooke has to set up 70 chairs in equal rows for the class talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?
Type below:
_________

Explanation:
Let the possible no.of rows be X, As there is no room for more than 20 rows so there should not be more than 20 rows.X should be less than or equal to 20 (X<=20).
As Brooke has 70 chairs to set up in equal rows we will find the factors of 70 and in that, we must pick up the numbers which are less than equal to 20.
Therefore the factors of 70 are 2,5,7,10,14.

Question 14.
Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of?
_________

Explanation:
If find factors for 1 to 20 we don’t get exactly 5 factors for any number except 16.
Thus Eduardo might be thinking of the number 16.

### Common Core – Factors, Multiples, and Patterns – Page No. 98

Lesson Check

Question 1.
Which of the following lists all the factors of 24?
Options:
a. 1, 4, 6, 24
b. 1, 3, 8, 24
c. 3, 4, 6, 8
d. 1, 2, 3, 4, 6, 8, 12, 24

Answer: 1, 2, 3, 4, 6, 8, 12, 24

Explanation:
Factors are the numbers that divide the original number completely.
Here, we can see the numbers which give the result as 24 when multiplied together.
1×24=24
2×12=24
3×8=24
4×6=24
6×4=4
8×3=24
12×2=24
24×1=24
So the factors of 24 are:1, 2, 3, 4, 6, 8, 12, 24.
Thus the correct answer is option d.

Question 2.
Natalia has 48 tiles. Which of the following shows a factor pair for the number 48?
Options:
a. 4 and 8
b. 6 and 8
c. 2 and 12
d. 3 and 24

Explanation:
Given that, Natalia has 48 tiles.
We have to find the factor pair of the number 48.
6 and 8 are factor pairs for 48 because 6×8=48.
Thus the correct answer is option b.

Spiral Review

Question 3.
The Pumpkin Patch is open every day. If it sells 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days?
Options:
a. 210 pounds
b. 2,100 pounds
c. 14,000 pounds
d. 21,000 pounds

Explanation:
Given that, The Pumpkin Patch is open every day.
Let’s round off 2750 pounds to 3000 pounds. In one day 3000 pounds pumpkins were sold out, and in
7 days?? —- 3000×7= 21,000 pounds.
It sold 21,000 pounds in 7 days.
Thus the correct answer is option d.

Question 4.
What is the remainder in the division problem modeled below? Options:
a. 2
b. 3
c. 5
d. 17

Explanation:
We can see in the above figure 3 circles with 5 sub circles inside it and a pair of sub circles.
Here total sub circles are (3×5)+2=17.
If we divide 17 with 3 then we will get a reminder as 2.
Thus the correct answer is option a.

Question 5.
Which number sentence is represented by the following array? Options:
a. 4 × 5 = 20
b. 4 × 4 = 16
c. 5 × 2 = 10
d. 5 × 5 = 25

Answer: 4 × 5 = 20

Explanation:
By seeing the above figure we can say that there are 4 rows and 5 columns.
As we can see 4 rows and 5 squares.
Multiply the number of rows with the number of columns.
So 4 × 5 = 20.
Thus the correct answer is option a.

Question 6.
Channing jogs 10 miles a week. How many miles will she jog in 52 weeks?
Options:
a. 30 miles
b. 120 miles
c. 200 miles
d. 520 miles

Explanation:
No.of weeks = 52. So 1 week = 10 miles,
then 52 weeks =?????
52 × 10 = 520 miles.
Thus the correct answer is option d.

### Common Core – Factors, Multiples, and Patterns – Page No. 99

Is 6 a factor of the number? Write yes or no.

Question 1. Question 2.
56
_____

Explanation:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56 .
56 is not divisible by 6.

Question 3.
42
_____

Explanation:
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.
Since 42 is divisible by 6.

Question 4.
66
_____

Explanation:
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
66 is divisible by 6.

Is 5 a factor of the number? Write yes or no.

Question 5.
38
_____

Explanation:
If the end is 0 or 5 then the number is divisible by 5.
The factors of 38 are 1, 2, 19, 38.
As the number is 38 the answer is No.

Question 6.
45
_____

Explanation:
45 is divisible by 5.
The factors of 45 are 1,3,5,9,15,45.

Question 7.
60
_____

Explanation:
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
60 is a factor of 5 because 60 is divisible by 5.

Question 8.
39
_____

Explanation:
The factors of 39 are 1,3,13,39.
As 39 is not divisible by 5.

List all the factor pairs

Question 9.
Factors of 12
_____ × _____ = 12; ( _____ , _____ )
_____ × _____ = 12; ( _____ , _____ )
_____ × _____ = 12; ( _____ , _____ )

1 × 12 = 12; ( 1 , 12 )
2 × 6 = 12; ( 2, 6 )
3 × 4 = 12; ( 3 , 4 )

Question 10.
Factors of 25
_____ × _____ = 25; ( _____ , _____ )
_____ × _____ = 25; ( _____ , _____ )

1 ×25 = 25; ( 1 , 25 )
5 × 5 = 25; ( 5 , 5 )

Question 11.
List all the factor pairs for 48.
Type below:
_________

Factor pairs of 48 are (1,48),(2,24),(3,16),(4,12),(6,8),(12,2),(6,3),(24,2),(48,1).

Explanation:
Factor pairs are the pairs when we multiplied both numbers will get the result. Here factor pairs for 48 are
1×48=48 (1,48)
2×24=48 (2,24)
3×16=48 (3,16)
4×12=48 (4,12)
6×8 =48 (6,8)

Problem Solving

Question 12.
Bryson buys a bag of 64 plastic miniature dinosaurs. Could he distribute them equally into six storage containers and not have any left over?
_____

Explanation:
Given that,
Bryson buys a bag of 64 plastic miniature dinosaurs.
64 is not divisible by 6, So he cannot distribute them equally into six storage containers.

Question 13.
Lori wants to distribute 35 peaches equally into baskets. She will use more than 1 but fewer than 10 baskets. How many baskets does Lori need?
Type below:
_________

Explanation:
First, we need to know the factors of 35.
The factors of 35 are 1,5,7,35. As Lori uses more than 1 but fewer than 10, the answer is 5 or 7. Lori can distribute 35 peaches equally in 5 or 7 baskets.

### Common Core – Factors, Multiples, and Patterns – Page No. 100

Lesson Check

Question 1.
Which of the following numbers has 9 as a factor?
Options:
a. 28
b. 30
c. 39
d. 45

Explanation:
45 is divisible 9.
Thus the correct answer is option d.

Question 2.
Which of the following numbers does NOT have 5 as a factor?
Options:
a. 15
b. 28
c. 30
d. 45

Explanation:
28 is not divisible by 5.
So 28 is not a factor of 5.
Thus the correct answer is option b.

Spiral Review

Question 3.
Which of the following shows a strategy to use to find 4 × 275?
Options:
a. (4 × 300) + (4 × 25)
b. (4 × 300) – (4 × 25)
c. (4 × 275) – 100
d. (4 × 200) + 75

Answer: (4 × 300) – (4 × 25)

Explanation:
First, we must replace 300-25 in the place of 275 then it becomes 4×(300-25), Now we must use the distributive property of multiplication then (4×300)-(4×25).

Question 4.
Jack broke apart 5 × 216 as (5 × 200) + (5 × 16) to multiply mentally. What strategy did Jack use?
Options:
a. the Commutative Property
b. the Associative Property
c. halving and doubling
d. the Distributive Property

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. This is the strategy Jack used.
Thus the correct answer is option d.

Question 5.
Jordan has $55. She earns$67 by doing chores. How much money does Jordan have now?
Options:
a. $122 b.$130
c. $112 d.$12

Answer: $122 Explanation: Jordan has$55, she earns by doing chores is $67. So the total money is$55+$67=$122.
Thus the correct answer is option a.

Question 6.
Trina has 72 collector’s stamps. She puts 43 of the stamps into a stamp book. How many stamps are left?
Options:
a. 29
b. 31
c. 39
d. 115

Explanation:
Given,
Trina has 72 collector’s stamps.
She puts 43 of the stamps into a stamp book.
Stamps left are 72-43=29.
Thus the correct answer is option a.

### Common Core – Factors, Multiples, and Patterns – Page No. 101

Problem Solving Common Factors

Solve each problem.

Question 1.
Grace is preparing grab bags for her store’s open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag? Question 2.
Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath?
Type below:
_________

Answer: 1,2,3,4,6 or 12 items Simon puts on each wreath.

Explanation:
Given that,
Simon is making wreaths to sell.
He has 60 bows, 36 silk roses, and 48 silk carnations.
He wants to put the same number of items on each wreath.
First we will find the common factors of 36,48,60
factors of 36 are: 1,2,3,4,6,9,12,18,36.
factors of 48 are: 1,2,3,4,6,8,12,16,24,48
factors of 60 are: 1,2,3,4,5,6,10,12,15,20,30,60.
The common factors of 36,48,60 are 1,2,3,4,6,12.
So Simon can put 1,2,3,4,6 or 12 items on each wreath.

Question 3.
Justin has 20 pencils, 25 erasers, and 40 paper clips. He organizes them into groups with the same number of items in each group. All the items in a group will be the same type. How many items can he put in each group?
Type below:
_________

Answer: Justin can put 1 or 5 items in each group.

Explanation:
Given,
Justin has 20 pencils, 25 erasers, and 40 paper clips.
He organizes them into groups with the same number of items in each group.
We will find common factors of 20,25,40.
factors of 20 are: 1,2,4,5,10,20.
factors of 25 are: 1,5,25.
factors of 40 are: 1,2,4,5,8,10,20,40
So common factors are 1 and 5.
Therefore, Justin can put 1 or 5 items in each group.

Question 4.
A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water. The volunteers will put the items into boxes. Each box will have the same number of food items and all the items in the box will be the same type. How many items can they put in each box?
Type below:
_________

Explanation:
Given,
A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water.
The volunteers will put the items into boxes.
1,2,5 or 10 are the common factors of 30,50 and 100.
factors for 30 are: 1,2,3,5,6,10,15,30
factors for 50 are: 1,2,5,10,25,50
factors of 100 are: 1,2,4,5,10,20,25,50,100

Question 5.
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy. All teams must have the same number of students. Each team can have only students from the same school. How many students can be on each team?
Type below:
_________

Explanation:
Given,
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy.
Lets find the common factors of 12,15,18
factors of 12 are: 1,2,3,4,6,12
factors of 15 are: 1,3,5,15
factors of 18 are: 1,2,3,6,9,18
3 is the common factor for 12,15,18
Therefore 3 students can be on each team.

### Common Core – Factors, Multiples, and Patterns – Page No. 102

Lesson Check

Question 1.
What are all the common factors of 24, 64, and 88?
Options:
a. 1 and 4
b. 1, 4, and 8
c. 1, 4, 8, and 12
d. 1, 4, 8, and 44

Explanation:
factors of 24 are: 1,2,3,4,8,12,24
factors of 64 are: 1,2,4,8,16,32,64
factors of 88 are: 1,2,4,8,11,22,44,88
Thus the correct answer is option b.

Question 2.
Which number is NOT a common factor of 15, 45, and 90?
Options:
a. 3
b. 5
c. 10
d. 15

Explanation:
As 15 and 45 are not divisible by 10.
Thus the correct answer is option c.

Spiral Review

Question 3.
Dan puts $11 of his allowance in his savings account every week. How much money will he have after 15 weeks? Options: a.$165
b. $132 c.$110
d. $26 Answer:$165

Explanation:
Dan puts $11 in his savings account every week. So after 15 weeks, it will be 15×11=165. The total money he will have after 15 weeks is$165.
Thus the correct answer is option a.

Question 4.
James is reading a book that is 1,400 pages. He will read the same number of pages each day. If he reads the book in 7 days, how many pages will he read each day?
Options:
a. 20
b. 50
c. 140
d. 200

Explanation:
Given,
James is reading a book that is 1,400 pages.
He will read the same number of pages each day.
Total no.of.pages is 1400, no.of pages James read each day is 1400÷7= 200
Thus the correct answer is option d.

Question 5.
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks. Which is the best estimate of the number of hours she volunteered each week?
Options:
a. 10 hours
b. 20 hours
c. 120 hours
d. 714 hours

Explanation:
Given,
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks.
Total hours Emma volunteered is 119 hours over 6 weeks.
To find:
how much she volunteered each week is
119÷6= 19.833 i.e 20 hours.
We must round off to the nearest one i.e 20 hours.
Thus the correct answer is option b.

Question 6.
Which strategy can be used to multiply 6 × 198 mentally?
Options:
a. 6 × 198 = (6 × 19) + (6 × 8)
b. 6 × 198 = (6 × 200) + (6 × 2)
c. 6 × 198 = (6 × 200) – (6 × 2)
d. 6 × 198 = (6 + 200) × (6 + 2)

Answer: 6 × 198 = (6 × 200) – (6 × 2)

Explanation:
By Distributive property of multiplication 6×198 can be written as (6 × 200) – (6 × 2).
Thus the correct answer is option c.

### Common Core – Factors, Multiples, and Patterns – Page No. 103

Factors and Multiples

Is the number a multiple of 8? Write yes or no.

Question 1. Question 2.
8
_____

Explanation: Since 8×1=8, it is a multiple of 8

Question 3.
20
_____

Explanation: 20 is not a multiple of 8

Question 4.
40
_____

Explanation: 8×5=40, So 40 is multiple of 8

List the next nine multiples of each number. Find the common multiples.

Question 5.
Multiples of 4:
Multiples of 7:
Common multiples:
Type below:
__________

Multiples of 4: 4,8,12,16,20,24,28,32,36,40.
Multiples of 7: 7,14,21,28,35,42,49,56,63,70.
Common Multiples: 28,

Question 6.
Multiples of 3:
Multiples of 9:
Common multiples:
Type below:
__________

Explanation:
Multiples of 3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63.
Multiples of 9: 9,18,27,36,45,54,63,72,81,90.
Common multiples: 9,18,45,54,63, etc.

Question 7.
Multiples of 6:
Multiples of 8:
Common multiples:
Type below:
__________

Explanation:
Multiples of 6: 6,12,18,24,30,36,42,48,54,60,66,72,78.
Multiples of 8: 8,16,24,32,40,48,56,64,72,80.
Common multiples: 24,48,72.

Tell whether 24 is a factor or multiple of the number. Write factor, multiple, or neither.

Question 8.
6
__________

Explanation: 6×4=24

Question 9.
36
__________

Explanation: 36 is not a factor or multiple of 24.

Question 10.
48
__________

Explanation: 24×2= 48, So 48 is a factor of 24

Problem Solving

Question 11.
Ken paid $12 for two magazines. The cost of each magazine was a multiple of$3. What are the possible prices of the magazines?
Type below:
__________

Answer: $3+$9=$12. Explanation: As each magazine cost was multiple of$3.
The possible price for 2 magazines are $3+$9=$12, which is a multiple of 3 Question 12. Jodie bought some shirts for$6 each. Marge bought some shirts for $8 each. The girls spent the same amount of money on shirts. What is the least amount they could have spent?$ _____

Answer: $24 Explanation: Given, Jodie bought some shirts for$6 each.
Marge bought some shirts for \$8 each.
The girls spent the same amount of money on shirts.
So multiples of 6 are: 6,12,18,24,30,36,42 and
multiples of 8 are: 8,16,24,32,40. The least amount they could spend is 24. As 24 is the least common multiple.

### Common Core – Factors, Multiples, and Patterns – Page No. 104

Lesson Check

Question 1.
Which list shows numbers that are all multiples of 4?
Options:
a. 2, 4, 6, 8
b. 3, 7, 11, 15, 19
c. 4, 14, 24, 34
d. 4, 8, 12, 16

Explanation:
Multiples of 4 are 4,8,12,16.
Thus the correct answer is option d.

Question 2.
Which of the following numbers is a common multiple of 5 and 9?
Options:
a. 9
b. 14
c. 36
d. 45

Explanation:
The common multiple of 5 and 9 is
5×9= 45
Thus the correct answer is option d.

Spiral Review

Question 3.
Jenny has 50 square tiles. She arranges the tiles into a rectangular array of 4 rows. How many tiles will be left over?
Options:
a. 0
b. 1
c. 2
d. 4

Explanation:
As Jenny arranges in 4 rows, each row contains 12 tiles.
So 12×4= 48.
The tiles left are 50 – 48 = 2.
Thus the correct answer is option c.

Question 4.
Jerome added two numbers. The sum was 83. One of the numbers was 45. What was the other number?
Options:
a. 38
b. 48
c. 42
d. 128

Explanation:
The sum of the two numbers is 83, in that one number is 45.
To find another number we will do subtraction,
i.e 83 – 45 = 38.
Thus the correct answer is option a.

Question 5.
There are 18 rows of seats in the auditorium. There are 24 seats in each row. How many seats are in the auditorium in all?
Options:
a. 42
b. 108
c. 412
d. 432

Explanation:
Given,
There are 18 rows of seats in the auditorium.
There are 24 seats in each row.
No.of rows= 18, each row has 24 seats.
So total no.of seats are 18×24= 432.
Thus the correct answer is option d.

Question 6.
The population of Riverdale is 6,735. What is the value of the 7 in the number 6,735?
Options:
a. 7
b. 700
c. 735
d. 7,000

Explanation:
Given,
The population of Riverdale is 6,735.
In 6,735 the 7 is in the Hundreds Place.
Thus the correct answer is option b.

### Common Core – Factors, Multiples, and Patterns – Page No. 105

Prime and Composite Numbers

Tell whether the number is prime or composite

Question 1. Question 2.
68
_________

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 68 are: 1,2,4,17,34,69.

Question 3.
52
_________

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 52 are: 1,2,4,13,26,52.

Question 4.
63
_________

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 63 are: 1,2,3,7,9,21,63.

Question 5.
75
_________

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 75 are: 1,3,5,15,25,75

Question 6.
31
_________

Explanation:
31 is a prime number that means it is divisible by 1 and itself.

Question 7.
77
_________

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 77 are 1,7,11,77.

Question 8.
59
_________

Explanation:
59 is a prime number that means it is divisible by 1 and itself.

Question 9.
87
_________

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 87 are: 1,3,29,87.

Question 10.
72
_________

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Question 11.
49
_________

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 49 are 1,7,49.

Question 12.
73
_________

Explanation:
A Prime number is a number that is divisible 1 and itself.

Problem Solving

Question 13.
Kai wrote the number 85 on the board. Is 85 prime or composite?
_________

Explanation: The number which has more than two factors is called composite numbers.
Factors of 85 are 1,5,17,85

Question 14.
Lisa says that 43 is a 2-digit odd number that is composite. Is she correct?
_____

Explanation:
43 is a prime number.
A Prime number is a number that is divisible 1 and itself.

### Common Core – Factors, Multiples, and Patterns – Page No. 106

Lesson Check

Question 1.
The number 5 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Explanation:
A Prime number is a number that is divisible 1 and itself.
Thus the correct answer is option a.

Question 2.
The number 1 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Explanation:
A Prime number is a number that is divisible 1 and itself. So prime number should have two divisors but 1 has only one divisor. The number which has more than two factors is called composite numbers. So 1 doesn’t have more than two factors. So 1 is neither Prime nor Composite.
Thus the correct answer is option d.

Spiral Review

Question 3.
A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving?
Options:
a. 134 calories
b. 150 calories
c. 154 calories
d. 231 calories

Explanation:
Total no.of calories are 924, which serves 6 people.
To find each serving we will perform division
924 ÷ 6 = 154 calories.
Thus the correct answer is option c.

Question 4.
A store clerk has 45 shirts to pack in boxes. Each box holds 6 shirts. What is the fewest boxes the clerk will need to pack all the shirts?
Options:
a. 9
b. 8
c. 7
d. 6

Explanation:
As the box holds only 6 shirts, 42 shirts are packed in 7 boxes, and the remaining 3 shirts will be packed in another box.
So the total number of boxes is 8.
Thus the correct answer is option b.

Question 5.
Which number rounds to 200,000?
Options:
a. 289,005
b. 251,659
c. 152,909
d. 149,889

Explanation:
152,909 is nearest to 200,000.
Thus the correct answer is option c.

Question 6.
What is the word form of the number 602,107?
Options:
a. six hundred twenty thousand,seventeen
b. six hundred two thousand, one hundred seven
c. six hundred twenty-one thousand, seventeen
d. six hundred two thousand, one hundred seventy

Answer: six hundred two thousand, one hundred seven

Explanation:
Convert the number 602,107 into the word form.
The word form of 602,107 is six hundred two thousand, one hundred seven
Thus the correct answer is option b.

### Common Core – Factors, Multiples, and Patterns – Page No. 107

Number Patterns

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 1. Question 2.
Rule: Subtract 7. First-term: 95
Type below:
_________

Explanation: 95
95-7= 88
88-7= 81
81-7= 74
74-7= 67
67-7= 60
60-7= 53
53-7= 46
46-7= 39
39-7= 32
32-7= 25
25-7= 18
18-7= 11

Question 3.
Rule: Add 15, subtract 10. First-term: 4
Type below:
_________

Explanation: 4
4+15= 19
19-10= 9
9+15= 24
24-10= 14
14+15= 29
29-10= 19
19+15= 34
34-10= 24
24+15= 39
39-10=29
29+15=44
44-10=34

Question 4.
Rule: Add 1, multiply by 2. First-term: 2
Type below:
_________

Explanation: 2
2+1= 2
2×2= 4
4+1= 5
5×2= 10
10+1= 11
11×2= 22
22+1= 23
23×2= 46
46+1= 47
47×2= 94
94+1= 95
95×2= 190.

Problem Solving

Question 5.
Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is the rule for the pattern?
Type below:
_________

Answer: The serial numbers of first 8 white beads are = 1, 5, 9, 13, 17, 21, 25, 29

Explanation:
Hence we can design the progression in the following way looking at the sequence:
W,B,B,B,W,B,B,B,W…….
Hence the required formula for white beads serial number is,
N = (X-1)(A+1) + L
Where, A = number of blue beads after each white beads = 3
L = initial position at which the first white bead is placed = 1
X = number of white bead
Putting the values in the above formula our equation becomes,
N = 4(X-1) + 1
Hence we can find out the serial numbers as follows:
N₁ = 4 x 0 + 1 = 1
N₂ = 4×1 + 1 = 5
N₃ = 4×2 + 1 = 9
and so on upto
N₈ = 4 x 7 + 1 = 29

Question 6.
An artist is arranging tiles in rows to decorate a wall. Each new row has 2 fewer tiles than the row below it. If the first row has 23 tiles, how many tiles will be in the seventh row?
_____ tiles

Explanation:
Given that,
An artist is arranging tiles in rows to decorate a wall.
Each new row has 2 fewer tiles than the row below it.
23
23-2= 21
21-2= 19
19-2= 17
17-2= 15
15-2= 13
13-2= 11

### Common Core – Factors, Multiples, and Patterns – Page No. 108

Lesson Check

Question 1.
The rule for a pattern is add 6. The first term is 5. Which of the following numbers is a term in the pattern?
Options:
a. 6
b. 12
c. 17
d. 22

Explanation:
Given that,
The rule for a pattern is add 6. The first term is 5.
5+6= 11
11+6= 17
Thus the correct answer is option c.

Question 2.
What are the next two terms in the pattern 3, 6, 5, 10, 9, 18, 17, . . .?
Options:
a. 16, 15
b. 30, 31
c. 33, 34
d. 34, 33

Explanation: 3
3×2= 6
6-1= 5
5×2= 10
10-1= 9
9×2= 18
18-1= 17
17×2= 34
34-1= 33
Thus the correct answer is option d.

Spiral Review

Question 3.
To win a game, Roger needs to score 2,000 points. So far, he has scored 837 points. How many more points does Roger need to score?
Options:
a. 1,163 points
b. 1,173 points
c. 1,237 points
d. 2,837 points

Explanation:
Roger has scored 837 points, He needs to score 2000 points to win, So to know how much more points do Roger needs we need to subtract i.e 2,000-837= 1,163.
Thus the correct answer is option a.

Question 4.
Sue wants to use mental math to find 7 × 53. Which expression could she use?
Options:
a. (7 × 5) + 3
b. (7 × 5) + (7 × 3)
c. (7× 50) + 3
d. (7 × 50) + (7 × 3)

Answer: (7 × 50) + (7 × 3)

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.
Thus the correct answer is option d.

Question 5.
Pat listed numbers that all have 15 as a multiple. Which of the following could be Pat’s list?
Options:
a. 1, 3, 5, 15
b. 1, 5, 10, 15
c. 1, 15, 30, 45
d. 15, 115, 215

Explanation:
Given,
Pat listed numbers that all have 15 as a multiple.
1×15= 15
3×5= 15
5×3= 15
15×1= 15
Thus the correct answer is option a.

Question 6.
Which is a true statement about 7 and 14?
Options:
a. 7 is a multiple of 14.
b. 14 is a factor of 7.
c. 14 is a common multiple of 7 and 14.
d. 21 is a common multiple of 7 and 14.

Answer: 14 is a common multiple of 7 and 14.

Explanation:
7×2=14
14×1=14
Thus the correct answer is option c.

### Common Core – Factors, Multiples, and Patterns – Page No. 109

Use tiles to find all the factors of the product. Record the arrays on grid paper and write the factors shown.

Question 1.
Write the factors of: 17
Type below:
_________

Answer: The factors of 17 are: 1, 17

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 17 when multiplied together.
1 × 17 = 17
17 × 1 = 17
So the factors of 17 are: 1, 17.

Question 2.
Write the factors of: 42
Type below:
_________

Answer: The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 42 when multiplied together.
1 × 42 = 42
2 × 21= 42
3 × 14 = 42
6 × 7 = 42
7 × 6 = 42
14 × 3 = 42
21 × 2 = 42
42 × 1 = 42
So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

Question 3.
Write the factors of: 28
Type below:
_________

Answer: The factors of 28 are: 1, 2, 4, 7, 14, 28.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 28 when multiplied together.
1 × 28 = 28
2 × 14 = 28
4 × 7 = 28
7 × 4 = 28
14 × 2 = 28
28 × 1 = 28
So the factors of 28 are:1, 2, 4, 7, 14, 28.

Question 4.
Write the factors of: 50
Type below:
_________

Answer: The factors of 50 are 1, 2, 5, 10, 25, and 50.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 50 when multiplied together.
1 × 50 = 50
2 × 25 = 50
5 × 10 = 50
10 × 5 = 50
25 × 2 = 50
50 × 1 = 50
The factors of 50 are 1, 2, 5, 10, 25, and 50.

Is 5 a factor of the number? Write yes or no.

Question 5.
35
_____

Explanation:
The factors of 35 are 1, 5, 7, 35. So, the answer is yes.

Question 6.
56
_____

Explanation:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. So, the answer is no.

Question 7.
51
_____

Explanation:
The factors of 51 are 1, 3, 17, 51. So, the answer is no.

Question 8.
40
_____

Explanation:
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. So, the answer is yes.

List all the factor pairs.

Question 9.
Factors of 16
_____ × _____ = 16; ( _____ , _____ )
_____ × _____ = 16; ( _____ , _____ )
_____ × _____ = 16; ( _____ , _____ )

Answer: The factor pairs of 16 are (1, 16), (2, 8), (4, 4)
1× 16 = 16; ( 1, 16)
2× 8 = 16; ( 2, 8)
4× 4 = 16; ( 4, 4)

Question 10.
Factors of 49
_____ × _____ = 49; ( _____ , _____ )
_____ × _____ = 49; ( _____ , _____ )

Answer: The factors in pairs of number 49 are (1, 49) and (7, 7).
1× 49= 49; ( 1, 49)
7× 7= 49; ( 7, 7)

Question 11.
Hana is putting the fruit she bought into bowls. She bought 8 melons, 12 pears, and 24 apples. She puts the same number of pieces of fruit in each bowl and puts only one type of fruit in each bowl. How many pieces can Hana put in each bowl?
Type below:
_________

If she wants the same number of pieces of each kind of fruit in each bowl (same number of melons, the same number of pears, and the same number of apples in each bowl), then she can put 11 pieces in each of the 4 bowls.

Explanation:
To answer this, we find the greatest common factor (GCF) of all 3 numbers. To do this, we find the prime factorization of 8, 12 and 24:
8 = 4 × 2
4 = 2 × 2
8 = 2 × 2× 2
12 = 4 × 3
4 = 2 × 2
12 = 2 × 2 × 3
24 = 4 × 6
4 = 2 × 2
6 = 2 × 3
24 = 2 × 2 × 2 × 3
The GCF is made of all of the common factors. The factors common to all 3 numbers are 2 and 2; 2(2) = 4 for the GCF.
This means we can use 4 bowls.
She has a total of 8+12+24 = 44 pieces of fruit; 44/4 = 11. She would have 11 pieces of fruit in each bowl.

Question 12.
A store owner is arranging clothing on racks. She has 30 sweaters, 45 shirts, and 15 pairs of jeans. She wants to put the same number of items on each rack, with only one type of item on each. How many items can she put on a rack?
Type below:
_________

I think what the teacher wants is 15 which is the greatest common factor of all three numbers and the factors of 15 are 1 x 15 and 3 x 5 so she can put one of each, or she can put 3 of each, or she can put 5 of each, or she can put 15 of each.

### Common Core – Factors, Multiples, and Patterns – Page No. 110

Is the number a multiple of 9? Write yes or no.

Question 1.
24
_____

Explanation:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. So the answer is no.

Question 2.
18
_____

Explanation:
The factors of 18 are 1, 2, 3, 6, 9, 18. So, the answer is yes.

Question 3.
27
_____

Explanation:
The factors of 27 are 1, 3, 9, 27. So, the answer is yes.

Question 4.
42
_____

Explanation:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. So the answer is no.

List the next nine multiples of each number.

Find the common multiples.

Question 5.
Multiples of 4:
Multiples of 5:
Common multiples:
Type below:
_________

Explanation:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
Common multiples: 20, 40.

Question 6.
Multiples of 3:
Multiples of 6:
Common multiples:
Type below:
_________

Answer: 6, 12, 18, 24, 30.

Explanation:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
Common multiples: 6, 12, 18, 24, 30.

Tell whether the number is prime or composite.

Question 7.
39
_____

Explanation: The number which has more than two factors is called composite numbers.
The factors of 39 are 1, 13, 39.
Thus 39 is the composite number.

Question 8.
29
_____

Explanation: A Prime number is a number that is divisible 1 and itself.
The factors of 29 are 1, 29.
So, 29 is the prime number.

Question 9.
51
_____

Explanation: The number which has more than two factors is called composite numbers.
The factors of 51 are 1, 3, 17, 51.
Therefore 51 is the composite number.

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 10.
Rule: Add 6. First term: 10
Type below:
_________

Answer: 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82.

Explanation: 10
10 + 6 = 16
16 + 6 = 22
22 + 6 = 28
28 + 6 = 34
34 + 6 = 40
40 + 6 = 46
46 + 6 = 52
52 + 6 = 58
58 + 6 = 64
64 + 6 = 70
70 + 6 = 76
76 + 6 = 82

Question 11.
Rule: Add 3, subtract 2. First term: 7
Type below:
_________

Answer: 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13.

Explanation: 7
7 + 3 = 10
10 – 2 = 8
8 + 3 = 11
11 – 2 = 9
9 + 3 = 12
12 – 2 = 10
10 + 3 = 13
13 – 2 = 11
11 + 3 = 14
14 – 2 = 12
12 + 3 = 15
15 – 2 = 13

Conclusion:

It is very difficult for parents to teach maths to primary school children. Keeping this in mind we have prepared the answers with step-by-step explanation in Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns. We suggest the students to Download Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns pdf and start your preparation. All the Best!!