What is the Greatest Common Factor of 31954 and 31972?

Greatest common factor (GCF) of 31954 and 31972 is 2.

GCF(31954,31972) = 2

We will now calculate the prime factors of 31954 and 31972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31954 and 31972.

How to find the GCF of 31954 and 31972?

We will first find the prime factorization of 31954 and 31972. After we will calculate the factors of 31954 and 31972 and find the biggest common factor number .

Step-1: Prime Factorization of 31954

Prime factors of 31954 are 2, 13, 1229. Prime factorization of 31954 in exponential form is:

31954 = 2¹ × 13¹ × 1229¹

Step-2: Prime Factorization of 31972

Prime factors of 31972 are 2, 7993. Prime factorization of 31972 in exponential form is:

31972 = 2² × 7993¹

Step-3: Factors of 31954

List of positive integer factors of 31954 that divides 31954 without a remainder.

1, 2, 13, 26, 1229, 2458, 15977

Step-4: Factors of 31972

List of positive integer factors of 31972 that divides 31954 without a remainder.

1, 2, 4, 7993, 15986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31954 and 31972. The biggest common factor number is the GCF number.
So the greatest common factor 31954 and 31972 is 2.

Also check out the Least Common Multiple of 31954 and 31972