eureka math grade 4 module 3 lesson 24 homework

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Eureka Math Grade 4 Module 3 Lesson 23 Answer Key

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)  and 82 + 1 = 83.

c. Is 3 a factor of 84? Answer: 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? Answer: 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? Answer: 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? Answer: 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? 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 or  0 in ones  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:  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_ 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__ × 4 = ( __3__ × 3) × 4 = __3__ × (3 × 4) = __3__ × 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 × 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 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 × 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,

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. Answer:  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. 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),  17 R1 2| 34  – 2   14   -14 0 Yes, 2 is a factor of 34.

b. Is 3 a factor of 34? Answer: 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? Answer: 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? Answer: 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. 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 × 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. 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),  36 2| 72  – 6   12   -12 0 Yes, 2 is a factor of 72.

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

c. Is 3 a factor of 72? Answer: Yes, 2 is a factor of 72,

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),  30 2| 60  – 60  0   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),  12 6| 72  – 6   12   -12 0 Yes, 6 is a factor of 72.

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),  15 4|60  -4   20   -20 0 Yes, 4 is a factor of 60.

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 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? 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),  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__ 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__ × 5 = ( __2__ × 3) × 5 = __2__ × (3 × 5) = __2__ × 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 × 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 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 × 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,

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. Answer:  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.

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