What is the Greatest Common Factor of 31948 and 31952?

Greatest common factor (GCF) of 31948 and 31952 is 4.

GCF(31948,31952) = 4

We will now calculate the prime factors of 31948 and 31952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31948 and 31952.

How to find the GCF of 31948 and 31952?

We will first find the prime factorization of 31948 and 31952. After we will calculate the factors of 31948 and 31952 and find the biggest common factor number .

Step-1: Prime Factorization of 31948

Prime factors of 31948 are 2, 7, 163. Prime factorization of 31948 in exponential form is:

31948 = 2² × 7² × 163¹

Step-2: Prime Factorization of 31952

Prime factors of 31952 are 2, 1997. Prime factorization of 31952 in exponential form is:

31952 = 2⁴ × 1997¹

Step-3: Factors of 31948

List of positive integer factors of 31948 that divides 31948 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 163, 196, 326, 652, 1141, 2282, 4564, 7987, 15974

Step-4: Factors of 31952

List of positive integer factors of 31952 that divides 31948 without a remainder.

1, 2, 4, 8, 16, 1997, 3994, 7988, 15976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31948 and 31952. The biggest common factor number is the GCF number.
So the greatest common factor 31948 and 31952 is 4.

Also check out the Least Common Multiple of 31948 and 31952