What is the Greatest Common Factor of 31964 and 31982?

Greatest common factor (GCF) of 31964 and 31982 is 2.

GCF(31964,31982) = 2

We will now calculate the prime factors of 31964 and 31982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31964 and 31982.

How to find the GCF of 31964 and 31982?

We will first find the prime factorization of 31964 and 31982. After we will calculate the factors of 31964 and 31982 and find the biggest common factor number .

Step-1: Prime Factorization of 31964

Prime factors of 31964 are 2, 61, 131. Prime factorization of 31964 in exponential form is:

31964 = 2² × 61¹ × 131¹

Step-2: Prime Factorization of 31982

Prime factors of 31982 are 2, 15991. Prime factorization of 31982 in exponential form is:

31982 = 2¹ × 15991¹

Step-3: Factors of 31964

List of positive integer factors of 31964 that divides 31964 without a remainder.

1, 2, 4, 61, 122, 131, 244, 262, 524, 7991, 15982

Step-4: Factors of 31982

List of positive integer factors of 31982 that divides 31964 without a remainder.

1, 2, 15991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31964 and 31982. The biggest common factor number is the GCF number.
So the greatest common factor 31964 and 31982 is 2.

Also check out the Least Common Multiple of 31964 and 31982