What is the Greatest Common Factor of 31965 and 31977?

Greatest common factor (GCF) of 31965 and 31977 is 3.

GCF(31965,31977) = 3

We will now calculate the prime factors of 31965 and 31977, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31965 and 31977.

How to find the GCF of 31965 and 31977?

We will first find the prime factorization of 31965 and 31977. After we will calculate the factors of 31965 and 31977 and find the biggest common factor number .

Step-1: Prime Factorization of 31965

Prime factors of 31965 are 3, 5, 2131. Prime factorization of 31965 in exponential form is:

31965 = 3¹ × 5¹ × 2131¹

Step-2: Prime Factorization of 31977

Prime factors of 31977 are 3, 11, 17, 19. Prime factorization of 31977 in exponential form is:

31977 = 3² × 11¹ × 17¹ × 19¹

Step-3: Factors of 31965

List of positive integer factors of 31965 that divides 31965 without a remainder.

1, 3, 5, 15, 2131, 6393, 10655

Step-4: Factors of 31977

List of positive integer factors of 31977 that divides 31965 without a remainder.

1, 3, 9, 11, 17, 19, 33, 51, 57, 99, 153, 171, 187, 209, 323, 561, 627, 969, 1683, 1881, 2907, 3553, 10659

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31965 and 31977. The biggest common factor number is the GCF number.
So the greatest common factor 31965 and 31977 is 3.

Also check out the Least Common Multiple of 31965 and 31977