1. Begin by writing the prime factorization of each number.
EXAMPLE 2
Using Prime Factorization to Find the GCF
Find the greatest common factor of 180 and 126 using prime factorization.
Begin by writing the prime factorization of each number.
180 = 2 3 5
126 = 2 3 7
ANSWER
The common prime factors of 180 and 126 are 2, 3, and 3. So, the greatest common factor is = 18.

2. EXAMPLE 2
Using Prime Factorization to Find the GCF
ANSWER
The common prime factors of 180 and 126 are 2, 3, and 3. So, the greatest common factor is = 18.

3. Tell whether the numbers are relatively prime.
EXAMPLE 3
Identifying Relatively Prime Numbers
Tell whether the numbers are relatively prime.
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 45: 1, 3, 5, 9, 15, 45
The GCF is 1.
a. 28, 45
ANSWER
Because the GCF is 1, 28 and 45 are relatively prime.
Factors of 15: 1, 3, 5, 15
Factors of 51: 1, 3, 17, 51
The GCF is 3.
b. 15, 51
ANSWER
Because the GCF is 3, 15 and 51 are not relatively prime.

4. GUIDED PRACTICE GUIDED PRACTICE
for Example 2 and 3
Find the greatest common factor of the numbers using prime factorization.
6. 90, 150
ANSWER 30
7. 84, 216
ANSWER 12
8. 120, 192
ANSWER 24
9. 49, 144
ANSWER 1

5. Tell whether the numbers are relatively prime.
GUIDED PRACTICE
GUIDED PRACTICE
for Example 2 and 3
Tell whether the numbers are relatively prime.
6. 13, 24
ANSWER
yes
7. 16, 25
ANSWER
yes
8. 38, 48
ANSWER no
9. 125, 175
ANSWER no