What is the Greatest Common Factor of 31971 and 31989?

Greatest common factor (GCF) of 31971 and 31989 is 3.

GCF(31971,31989) = 3

We will now calculate the prime factors of 31971 and 31989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31971 and 31989.

How to find the GCF of 31971 and 31989?

We will first find the prime factorization of 31971 and 31989. After we will calculate the factors of 31971 and 31989 and find the biggest common factor number .

Step-1: Prime Factorization of 31971

Prime factors of 31971 are 3, 10657. Prime factorization of 31971 in exponential form is:

31971 = 3¹ × 10657¹

Step-2: Prime Factorization of 31989

Prime factors of 31989 are 3, 10663. Prime factorization of 31989 in exponential form is:

31989 = 3¹ × 10663¹

Step-3: Factors of 31971

List of positive integer factors of 31971 that divides 31971 without a remainder.

1, 3, 10657

Step-4: Factors of 31989

List of positive integer factors of 31989 that divides 31971 without a remainder.

1, 3, 10663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31971 and 31989. The biggest common factor number is the GCF number.
So the greatest common factor 31971 and 31989 is 3.

Also check out the Least Common Multiple of 31971 and 31989