Question

5-5 (a): greatest common factor (gcf)
find the gcf of each set of numbers.

1. 15, 40
2. 16, 36
3. 12, 54
4. 24, 64
5. 39, 26
6. 35, 63
7. 36, 48
8. 35, 28
9. 12, 30
10. monlque has the flowers shown in the table. she wants to put all the flowers into decorative vases. each vase must have the same number of flowers in it. without mixing flowers, what is the greatest number of flowers that monique can put in each vase?

flower type	number
roses	25

Explanation:

Problem 5: 39, 26

Step1: Factorize 39 and 26

Prime factors of \( 39 = 3\times13 \)
Prime factors of \( 26 = 2\times13 \)

Step2: Identify common factors

The common prime factor is \( 13 \). So the GCF is \( 13 \).

Step1: Factorize 35 and 63

Prime factors of \( 35 = 5\times7 \)
Prime factors of \( 63 = 7\times9 = 7\times3\times3 \)

Step2: Identify common factors

The common prime factor is \( 7 \). So the GCF is \( 7 \).

Step1: Factorize 36 and 48

Prime factors of \( 36 = 2\times2\times3\times3 \)
Prime factors of \( 48 = 2\times2\times2\times2\times3 \)

Step2: Identify common factors

The common prime factors are \( 2\times2\times3 = 12 \). So the GCF is \( 12 \).

Answer:

\( 13 \)

Problem 6: 35, 63