Question

1. determine all the factors of each number.

a 16 b 25
c 100 d 37

1. for the numbers 20 and 24, determine each of the following.

a the factors of 20.
b the factors of 24.
c the common factors of 20 and 24.
d the gcf of 20 and 24.

1. for the numbers 18 and 27, determine each of the following.

a the factors of 18.
b the factors of 27.
c the common factors of 18 and 27.
d the gcf of 18 and 27.

1. determine the gcf for each pair of numbers. explain your thinking.

a 33 and 15 b 8 and 32
c 45 and 54 d 35 and 21

Explanation:

Step1: List factors of 16

Find pairs multiplying to 16: $1 \times 16$, $2 \times 8$, $4 \times 4$

Step2: List factors of 25

Find pairs multiplying to 25: $1 \times 25$, $5 \times 5$

Step3: List factors of 100

Find pairs multiplying to 100: $1 \times 100$, $2 \times 50$, $4 \times 25$, $5 \times 20$, $10 \times 10$

Step4: List factors of 37

37 is prime: $1 \times 37$

Step5: List factors of 20

Find pairs multiplying to 20: $1 \times 20$, $2 \times 10$, $4 \times 5$

Step6: List factors of 24

Find pairs multiplying to 24: $1 \times 24$, $2 \times 12$, $3 \times 8$, $4 \times 6$

Step7: Find common factors of 20,24

Identify shared values from Step5/6

Step8: Find GCF of 20,24

Largest value from Step7

Step9: List factors of 18

Find pairs multiplying to 18: $1 \times 18$, $2 \times 9$, $3 \times 6$

Step10: List factors of 27

Find pairs multiplying to 27: $1 \times 27$, $3 \times 9$

Step11: Find common factors of 18,27

Identify shared values from Step9/10

Step12: Find GCF of 18,27

Largest value from Step11

Step13: Find GCF of 33,15

List factors: 33: {1,3,11,33}; 15: {1,3,5,15}. Largest shared value.

Step14: Find GCF of 8,32

List factors: 8: {1,2,4,8}; 32: {1,2,4,8,16,32}. Largest shared value.

Step15: Find GCF of 45,54

List factors: 45: {1,3,5,9,15,45}; 54: {1,2,3,6,9,18,27,54}. Largest shared value.

Step16: Find GCF of 35,21

List factors: 35: {1,5,7,35}; 21: {1,3,7,21}. Largest shared value.

Answer:

1.
a. 1, 2, 4, 8, 16
b. 1, 5, 25
c. 1, 2, 4, 5, 10, 20, 25, 50, 100
d. 1, 37

2.
a. 1, 2, 4, 5, 10, 20
b. 1, 2, 3, 4, 6, 8, 12, 24
c. 1, 2, 4
d. 4

3.
a. 1, 2, 3, 6, 9, 18
b. 1, 3, 9, 27
c. 1, 3, 9
d. 9

4.
a. GCF = 3; The common factors of 33 and 15 are 1 and 3, so the largest is 3.
b. GCF = 8; 8 is a factor of 32, so it is the greatest common factor.
c. GCF = 9; The common factors of 45 and 54 are 1, 3, 9, so the largest is 9.
d. GCF = 7; The common factors of 35 and 21 are 1 and 7, so the largest is 7.