What is the Greatest Common Factor of 31968 and 31974?

Greatest common factor (GCF) of 31968 and 31974 is 6.

GCF(31968,31974) = 6

We will now calculate the prime factors of 31968 and 31974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31968 and 31974.

How to find the GCF of 31968 and 31974?

We will first find the prime factorization of 31968 and 31974. After we will calculate the factors of 31968 and 31974 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31974

Prime factors of 31974 are 2, 3, 73. Prime factorization of 31974 in exponential form is:

31974 = 2¹ × 3¹ × 73²

Step-3: Factors of 31968

List of positive integer factors of 31968 that divides 31968 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

Step-4: Factors of 31974

List of positive integer factors of 31974 that divides 31968 without a remainder.

1, 2, 3, 6, 73, 146, 219, 438, 5329, 10658, 15987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31968 and 31974. The biggest common factor number is the GCF number.
So the greatest common factor 31968 and 31974 is 6.

Also check out the Least Common Multiple of 31968 and 31974