What is the Greatest Common Factor of 975 and 988?

Greatest common factor (GCF) of 975 and 988 is 13.

GCF(975,988) = 13

We will now calculate the prime factors of 975 and 988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 975 and 988.

How to find the GCF of 975 and 988?

We will first find the prime factorization of 975 and 988. After we will calculate the factors of 975 and 988 and find the biggest common factor number .

Step-1: Prime Factorization of 975

Prime factors of 975 are 3, 5, 13. Prime factorization of 975 in exponential form is:

975 = 3¹ × 5² × 13¹

Step-2: Prime Factorization of 988

Prime factors of 988 are 2, 13, 19. Prime factorization of 988 in exponential form is:

988 = 2² × 13¹ × 19¹

Step-3: Factors of 975

List of positive integer factors of 975 that divides 975 without a remainder.

1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325

Step-4: Factors of 988

List of positive integer factors of 988 that divides 975 without a remainder.

1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 975 and 988. The biggest common factor number is the GCF number.
So the greatest common factor 975 and 988 is 13.

Also check out the Least Common Multiple of 975 and 988