What is the Greatest Common Factor of 31952 and 31968?

Greatest common factor (GCF) of 31952 and 31968 is 16.

GCF(31952,31968) = 16

We will now calculate the prime factors of 31952 and 31968, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31952 and 31968.

How to find the GCF of 31952 and 31968?

We will first find the prime factorization of 31952 and 31968. After we will calculate the factors of 31952 and 31968 and find the biggest common factor number .

Step-1: Prime Factorization of 31952

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

31952 = 2⁴ × 1997¹

Step-2: Prime Factorization of 31968

Prime factors of 31968 are 2, 3, 37. Prime factorization of 31968 in exponential form is:

31968 = 2⁵ × 3³ × 37¹

Step-3: Factors of 31952

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

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

Step-4: Factors of 31968

List of positive integer factors of 31968 that divides 31952 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 37, 48, 54, 72, 74, 96, 108, 111, 144, 148, 216, 222, 288, 296, 333, 432, 444, 592, 666, 864, 888, 999, 1184, 1332, 1776, 1998, 2664, 3552, 3996, 5328, 7992, 10656, 15984

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31952 and 31968. The biggest common factor number is the GCF number.
So the greatest common factor 31952 and 31968 is 16.

Also check out the Least Common Multiple of 31952 and 31968