What is the Greatest Common Factor of 969 and 975?

Greatest common factor (GCF) of 969 and 975 is 3.

GCF(969,975) = 3

We will now calculate the prime factors of 969 and 975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 969 and 975.

How to find the GCF of 969 and 975?

We will first find the prime factorization of 969 and 975. After we will calculate the factors of 969 and 975 and find the biggest common factor number .

Step-1: Prime Factorization of 969

Prime factors of 969 are 3, 17, 19. Prime factorization of 969 in exponential form is:

969 = 3¹ × 17¹ × 19¹

Step-2: 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-3: Factors of 969

List of positive integer factors of 969 that divides 969 without a remainder.

1, 3, 17, 19, 51, 57, 323

Step-4: Factors of 975

List of positive integer factors of 975 that divides 969 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 969 and 975. The biggest common factor number is the GCF number.
So the greatest common factor 969 and 975 is 3.

Also check out the Least Common Multiple of 969 and 975