What is the Greatest Common Factor of 31971 and 31983?

Greatest common factor (GCF) of 31971 and 31983 is 3.

GCF(31971,31983) = 3

We will now calculate the prime factors of 31971 and 31983, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31971 and 31983.

How to find the GCF of 31971 and 31983?

We will first find the prime factorization of 31971 and 31983. After we will calculate the factors of 31971 and 31983 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 31983

Prime factors of 31983 are 3, 7, 1523. Prime factorization of 31983 in exponential form is:

31983 = 3¹ × 7¹ × 1523¹

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 31983

List of positive integer factors of 31983 that divides 31971 without a remainder.

1, 3, 7, 21, 1523, 4569, 10661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31971 and 31983. The biggest common factor number is the GCF number.
So the greatest common factor 31971 and 31983 is 3.

Also check out the Least Common Multiple of 31971 and 31983