## 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.
a. Is 2 a factor of 84?
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?
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)  and 82 + 1 = 83.

c. Is 3 a factor of 84?
Yes, 3 is a factor of 84,

Explanation:
28
3| 84
-6
24
-24
0
So 3 is a factor of 84.

d. Is 2 a factor of 92?
Yes, 2 is a factor of 92 and 92 is even number,

Explanation:
46
2| 92
– 8
12
-12
0
So 2 is a factor of 92.

e. Is 6 a factor of 84?
Yes, 6 is a factor of 84 and 84 is even number,

Explanation:
14
6| 84
– 6
24
-24
0
So 6 is a factor of 84.

f. Is 4 a factor of 92?
Yes, 4 is a factor of 92,

Explanation:
23
4| 92
– 8
12
-12
0
So 4 is a factor of 92.

g. Is 5 a factor of 84?
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 or  0 in ones  place,
So 5 is not a factor of 84.

h. Is 8 a factor of 92?
No, 8 is not a factor of 92,

Explanation:
11 R4
8| 92
– 8
12
-08
04
So 8 is not a factor of 92 remainder is 4.

Question 2.
Use the associative property to find more factors of 24 and 36.
a. 24 = 12 × 2
= ( _4__ × 3) × 2
= __4_ × (3 × 2)
= _4__ × 6
= __24_
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__ × 4
= ( __3__ × 3) × 4
= __3__ × (3 × 4)
= __3__ × 12
= _36__
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 × 3.
Use the fact that 8 = 4 × 2 to show that 2 and 4 are factors of 56, 72, and 80.
56 = 8 × 7        72 = 8 × 9        80 = 8 × 10
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 × 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 × 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 × 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.
14
2|28
-2
08
-08
0
2 X 14 = 28,
7
4|28
-28
0
4 X 7 = 28,
3, R4
8|28
-24
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,
14
2|28
-2
08
-08
0
2 X 14 = 28,
7
4|28
-28
0
4 X 7 = 28,
3, R4
8|28
-24
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.
a. Is 2 a factor of 34?
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),
17 R1
2| 34
– 2
14
-14
0
Yes, 2 is a factor of 34.

b. Is 3 a factor of 34?
No, 3 is not a factor of 34,

Explanation:
11 R1
3| 34
– 3
04
-03
01
So 3 is not a factor of 34 remainder is 1.

c. Is 4 a factor of 72?
Yes, 4 is a factor of 72,

Explanation:
18
4| 72
– 4
32
-32
0
So 4 is a factor of 72.

d. Is 3 a factor of 72?
Yes, 3 is a factor of 72,

Explanation:
24
3| 72
– 6
12
-12
0
So 3 is a factor of 72.

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.
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 × 3, we can also write N as N = 3 × 3 × M,
That means N is 3 times some integer (3 × M).
So 3 is also a factor of N.

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

Question 1.
a. Is 2 a factor of 72?
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),
36
2| 72
– 6
12
-12
0
Yes, 2 is a factor of 72.

b. Is 2 a factor of 73?
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
36 R 1
2| 73
– 6
13
-12
1
No, 2 is not a factor of 73.

c. Is 3 a factor of 72?
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),
36
2| 72
– 6
12
-12
0
Yes, 2 is a factor of 72.

d. Is 2 a factor of 60?
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),
30
2| 60
– 60
0
Yes, 2 is a factor of 60.

e. Is 6 a factor of 72?
Yes, 6 is a factor of 72,

Explanation:
(6 X 12 = 72),
12
6| 72
– 6
12
-12
0
Yes, 6 is a factor of 72.

f. Is 4 a factor of 60?
Yes, 4 is a factor of 60,

Explanation:
60 is a even number, 4 is a factor of 60, (4 X 15 = 60),
15
4|60
-4
20
-20
0
Yes, 4 is a factor of 60.

g. Is 5 a factor of 72?
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 or  0 in ones  place,
So 5 is not a factor of 72.
14 R 2
5|72
-5
22
-20
2
No, 5 is not a factor of 72.

h. Is 8 a factor of 60?
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),
7 R 4
8|60
-56
04
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 × 2
= ( __3_ × 2) × 2
= _3__ × (2 × 2)
= _3__ × _4__
= _12__
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__ × 5
= ( __2__ × 3) × 5
= __2__ × (3 × 5)
= __2__ × 15
= __30__
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 × 3.
Use the fact that 10 = 5 × 2 to show that 2 and 5 are factors of 70, 80, and 90.
70 = 10 × 7          80 = 10 × 8       90 = 10 × 9
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 × 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 × 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 × 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.
9
2|18
-18
0
2 X 9 = 18,
3
6|18
-18
0
6 X 3 = 18,
1, R6
12|18
– 12
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,
9
2|18
-18
0
2 X 9 = 18,
3
6|18
-18
0
6 X 3 = 18,
1, R6
12|18
– 12
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.