What is the GCF of 75 and 30?

Answer 1

The greatest common factor of 30 and 75 is 15.

Method 1: Listing Factors

List all the factors of both numbers and the highest factor that is the same is the greatest common factor.

Factors of 30: 1, 2, 3, 5, 6, 10, 15

Factors of 75: 1, 3, 5, 15, 25

The greatest common factor is 15.

Method 2: Prime Factorization

Find the prime factorization of each number. The prime numbers that the numbers all share multiply to the great common factor.

30=2*3*5

75=3*5*5

3*5=15

30 and 75 share one 3 and one 5. Therefore, the greatest common factor is 15.