## Engage NY Eureka Math 4th Grade Module 3 Lesson 23 Answer Key

### Eureka Math Grade 4 Module 3 Lesson 23 Problem Set Answer Key

Question 1.

Explain your thinking or use division to answer the following.

a. Is 2 a factor of 84?

Answer:

Yes, 2 is a factor of 84,

Explanation:

84 is a even number, 2 is a factor of every even number, ( 2 X 42 = 84).

b. Is 2 a factor of 83?

Answer:

No, 2 is not a factor of 83,

Explanation:

83 is a odd number, 2 is not a factor of odd numbers, So 2 is not a factor of 83,

(2 X 41 = 82)Â and 82 + 1 = 83.

c. Is 3 a factor of 84?

Answer:

Yes, 3 is a factor of 84,

Explanation:

Â Â 28

3| 84

Â -6

Â 24Â Â

-24

0

So 3 is a factor of 84.

d. Is 2 a factor of 92?

Answer:

Yes, 2 is a factor of 92 and 92 is even number,

Explanation:

Â 46

2| 92

Â – 8

Â 12Â Â

-12

0

So 2 is a factor of 92.

e. Is 6 a factor of 84?

Answer:

Yes, 6 is a factor of 84 and 84 is even number,

Explanation:

Â 14

6| 84

Â – 6

Â 24Â Â

-24

0

So 6 is a factor of 84.

f. Is 4 a factor of 92?

Answer:

Yes, 4 is a factor of 92,

Explanation:

__Â 23
__4| 92

__Â – 8__

Â 12Â Â

__So 4 is a factor of 92.__

-12

0

-12

0

g. Is 5 a factor of 84?

Answer:

No, 5 is not a factor of 84,

Explanation:

84 does not have 5 or 0 in ones place, all the numbers that have 5 as a factor have a 5 orÂ 0 in onesÂ place,

So 5 is not a factor of 84.

h. Is 8 a factor of 92?

Answer:

No, 8 is not a factor of 92,

Explanation:

__Â 11 R4
__8| 92

__Â – 8__

Â 12Â Â

__So 8 is not a factor of 92 remainder is 4.__

-08

04

-08

04

Question 2.

Use the associative property to find more factors of 24 and 36.

a. 24 = 12 Ã— 2

= ( _4__ Ã— 3) Ã— 2

= __4_ Ã— (3 Ã— 2)

= _4__ Ã— 6

= __24_

Answer:

24 = 12 X 2

= (4 X 3) X 2

= 4 X (3 X 2)

= 4 X 6

= 24,

Explanation:

Used the associative property to find more factors of 24 as

24 = 12 X 2

= (4 X 3) X 2

= 4 X (3 X 2)

= 4 X 6

= 24.

b. 36 = __9__ Ã— 4

= ( __3__ Ã— 3) Ã— 4

= __3__ Ã— (3 Ã— 4)

= __3__ Ã— 12

= _36__

Answer:

36 = 9 X 4

= (3 X 3) X 4

= 3 X (3 X 4)

= 3 X 12

= 36,

Explanation:

Used the associative property to find more factors of 36 as

36 = 9 X 4

= (3 X 3) X 4

= 3 X (3 X 4)

= 3 X 12

= 36.

Question 3.

In class, we used the associative property to show that when 6 is a factor, then 2 and 3 are factors, because 6 = 2 Ã— 3.

Use the fact that 8 = 4 Ã— 2 to show that 2 and 4 are factors of 56, 72, and 80.

56 = 8 Ã— 7Â Â Â Â 72 = 8 Ã— 9Â Â Â Â 80 = 8 Ã— 10

Answer:

56 = 8 X 7

= (4 X 2) X 7

= 4 X (2 X 7)

= 4 X 14

= 56,

72 = 8 X 9

= 8 X 9

= (4 X 2) X 9

= 4 X (2 X 9)

= 4 X 18

= 72,

80 = 8 Ã— 10

= 8 X 10

= (4 X 2) X 10

= 4 X (2 X 10)

= 4 X 20

= 80,

Explanation:

Used the fact that 8 = 4 Ã— 2 to showed that 2 and 4 are factors of 56, 72, and 80 as

56 = 8 X 7

= (4 X 2) X 7

= 4 X (2 X 7)

= 4 X 14

= 56,

72 = 8 X 9

= 8 X 9

= (4 X 2) X 9

= 4 X (2 X 9)

= 4 X 18

= 72,

80 = 8 Ã— 10

= 8 X 10

= (4 X 2) X 10

= 4 X (2 X 10)

= 4 X 20

= 80.

Question 4.

The first statement is false. The second statement is true. Explain why, using words, pictures, or numbers. If a number has 2 and 4 as factors, then it has 8 as a factor. If a number has 8 as a factor, then both 2 and 4 are factors.

Answer:

Â 14

2|28

Â -2

Â Â 08

Â -08

0

2 X 14 = 28,

Â 7

4|28

Â -28

Â Â 0

4 X 7 = 28,

Â Â 3, R4

8|28

Â -24

Â Â 04

28 has 2 and 4 as factors but not 8,

Explanation:

The first statement is false. The second statement is true. If a number has 2 and 4 as factors, then it has 8 as a factor and If a number has 8 as a factor, then both 2 and 4 are factors,

Â 14

2|28

Â -2

Â Â 08

Â -08

0

2 X 14 = 28,

Â 7

4|28

Â -28

Â Â 0

4 X 7 = 28,

Â Â 3, R4

8|28

Â -24

Â Â 04

28 has 2 and 4 as factors but not 8, any number that can be divided exactly by 8 can also be divided by 2 and 4 instead, Since 8 = 2 X 4,

Example: 8 X 5 = 40, (4 X 2) X 5 = 40.

### Eureka Math Grade 4 Module 3 Lesson 23 Exit Ticket Answer Key

Question 1.

Explain your thinking or use division to answer the following.

a. Is 2 a factor of 34?

Answer:

Yes, 2 is a factor of 34,

Explanation:

34 is a even number, 2 is a factor of every even

number, (2 X 17 = 34),

__Â 17 R1
__2| 34

__Â – 2__

Â 14Â Â

__Yes, 2 is a factor of 34.__

-14

0

-14

0

b. Is 3 a factor of 34?

Answer:

No, 3 is not a factor of 34,

Explanation:

__Â 11 R1
__3| 34

__Â – 3__

Â 04Â Â

__So 3 is not a factor of 34 remainder is 1.__

-03

01

-03

01

c. Is 4 a factor of 72?

Answer:

Yes, 4 is a factor of 72,

Explanation:

__Â 18
__4| 72

__Â – 4__

Â 32Â Â

__So 4 is a factor of 72.__

-32

0

-32

0

d. Is 3 a factor of 72?

Answer:

Yes, 3 is a factor of 72,

Explanation:

__Â 24
__3| 72

__Â – 6__

Â 12Â Â

__So 3 is a factor of 72.__

-12

0

-12

0

Question 2.

Use the associative property to explain why the following statement is true. Any number that has 9 as a factor also has 3 as a factor.

Answer:

Any number that has 9 as a factor also has 3 as a factor because 3 X 3 = 9,

Explanation:

Let’s suppose 9 is a factor of the number N.

That means N is 9 times some integer M.

N = 9M, Since 9 = 3 Ã— 3, we can also write N as N = 3 Ã— 3 Ã— M,

That means N is 3 times some integer (3 Ã— M).

So 3 is also a factor of N.

### Eureka Math Grade 4 Module 3 Lesson 23 Homework Answer Key

Question 1.

Explain your thinking or use division to answer the following.

a. Is 2 a factor of 72?

Answer:

Yes, 2 is a factor of 72,

Explanation:

72 is a even number, 2 is a factor of every even number, (2 X 36 = 72),

__Â 36
__2| 72

__Â – 6__

Â 12Â Â

__Yes, 2 is a factor of 72.__

-12

0

-12

0

b. Is 2 a factor of 73?

Answer:

No, 2 is not a factor of 73,

Explanation:

73 is a odd number, 2 is a factor of every even number not odd numbers, (2 X 36 = 72),72 + 1 = 73

__Â 36 R 1
__2| 73

__Â – 6__

Â 13Â Â

__No, 2 is not a factor of 73.__

-12

1

-12

1

c. Is 3 a factor of 72?

Answer:

Yes, 2 is a factor of 72,

Explanation:

72 is a even number, 2 is a factor of every even number, (2 X 36 = 72),

__Â 36
__2| 72

__Â – 6__

Â 12Â Â

__Yes, 2 is a factor of 72.__

-12

0

-12

0

d. Is 2 a factor of 60?

Answer:

Yes, 2 is a factor of 60,

Explanation:

60 is a even number, 2 is a factor of every even number, (2 X 30 = 60),

__Â 30
__2| 60

__Â – 60__

Â 0Â Â

__Yes, 2 is a factor of 60.__

e. Is 6 a factor of 72?

Answer:

Yes, 6 is a factor of 72,

Explanation:

(6 X 12 = 72),

__Â 12
__6| 72

__Â – 6__

Â 12Â Â

__Yes, 6 is a factor of 72.__

-12

0

-12

0

f. Is 4 a factor of 60?

Answer:

Yes, 4 is a factor of 60,

Explanation:

60 is a even number, 4 is a factor of 60, (4 X 15 = 60),

__Â 15
__4|60

__Â -4__

Â 20Â Â

__Yes, 4 is a factor of 60.__

-20

0

-20

0

g. Is 5 a factor of 72?

Answer:

No, 5 is not a factor of 72,

Explanation:

72 is a even number, 72 does not have 5 or 0 in ones place, all the numbers that have 5 as a factor have a 5 orÂ 0 in onesÂ place,

So 5 is not a factor of 72.

__Â 14 R 2
__5|72

__Â -5__

Â 22Â Â

__No, 5 is not a factor of 72.__

-20

2

-20

2

h. Is 8 a factor of 60?

Answer:

No, 8 is not a factor of 60,

Explanation:

60 is a even number, 8 is not a factor of 60,

(8 X 7 = 56, remainder 4),

__Â 7 R 4
__8|60

__Â -56__

Â 04Â Â

__No, 8 is not a factor of 60.__

Question 2.

Use the associative property to find more factors of 12 and 30.

a. 12 = 6 Ã— 2

= ( __3_ Ã— 2) Ã— 2

= _3__ Ã— (2 Ã— 2)

= _3__ Ã— _4__

= _12__

Answer:

12 = 6 X 2

= (3 X 2) X 2

= 3 X (2 X 2)

= 3 X 4

= 12,

Explanation:

Used the associative property to find more factors of 12 as

12 = 6 X 2

= (3 X 2) X 2

= 3 X (2 X 2)

= 3 X 4

= 12.

b. 30 = __6__ Ã— 5

= ( __2__ Ã— 3) Ã— 5

= __2__ Ã— (3 Ã— 5)

= __2__ Ã— 15

= __30__

Answer:

30 = 6 X 5

= (2 X 3) X 5

= 2 X (3 X 5)

= 2 X 15

= 30,

Explanation:

Used the associative property to find more factors of 30 as

30 = 6 X 5

= (2 X 3) X 5

= 2 X (3 X 5)

= 2 X 15

= 30.

Question 3.

In class, we used the associative property to show that when 6 is a factor, then 2 and 3 are factors, because 6 = 2 Ã— 3.

Use the fact that 10 = 5 Ã— 2 to show that 2 and 5 are factors of 70, 80, and 90.

70 = 10 Ã— 7Â Â Â Â Â 80 = 10 Ã— 8Â Â Â Â 90 = 10 Ã— 9

Answer:

70 = 10 X 7

= (5 X 2) X 7

= 5 X (2 X 7)

= 5 X 14

= 70,

80 = 10 X 8

= 10 X 8

= (5 X 2) X 8

= 5 X (2 X 8)

= 5 X 16

= 80,

90 = 10 Ã— 9

= 10 X 9

= (5 X 2) X 9

= 5 X (2 X 9)

= 5 X 18

= 90,

Explanation:

Used the fact that 10 = 5 Ã— 2 to showed that 2 and 5 are factors of 70, 80, and 90 as

70 = 10 X 7

= (5 X 2) X 7

= 5 X (2 X 7)

= 5 X 14

= 70,

80 = 10 X 8

= 10 X 8

= (5 X 2) X 8

= 5 X (2 X 8)

= 5 X 16

= 80,

90 = 10 Ã— 9

= 10 X 9

= (5 X 2) X 9

= 5 X (2 X 9)

= 5 X 18

= 90.

Question 4.

The first statement is false. The second statement is true.

Explain why, using words, pictures, or numbers. If a number has 2 and 6 as factors, then it has 12 as a factor. If a number has 12 as a factor, then both 2 and 6 are factors.

Answer:

Â 9

2|18

Â -18

0

2 X 9 = 18,

Â 3

6|18

Â -18

Â Â 0

6 X 3 = 18,

Â Â 1, R6

12|18

Â – 12

Â Â 06

18 has 2 and 6 as factors but not 12,

Explanation:

The first statement is false. The second statement is true. If a number has 2 and 6 as factors, then it has 12 as a factor and If a number has 12 as a factor, then both 2 and 6 are factors,

Â 9

2|18

Â -18

0

2 X 9 = 18,

Â 3

6|18

Â -18

Â Â 0

6 X 3 = 18,

Â Â 1, R6

12|18

Â – 12

Â Â 06

18 has 2 and 6 as factors but not 12, any number that can be divided exactly by 12 can also be divided by 2 and 6 instead, Since 12 = 2 X 6.