What is the Greatest Common Factor of 31959 and 31968?

Greatest common factor (GCF) of 31959 and 31968 is 9.

GCF(31959,31968) = 9

We will now calculate the prime factors of 31959 and 31968, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31959 and 31968.

How to find the GCF of 31959 and 31968?

We will first find the prime factorization of 31959 and 31968. After we will calculate the factors of 31959 and 31968 and find the biggest common factor number .

Step-1: Prime Factorization of 31959

Prime factors of 31959 are 3, 53, 67. Prime factorization of 31959 in exponential form is:

31959 = 3² × 53¹ × 67¹

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 31959

List of positive integer factors of 31959 that divides 31959 without a remainder.

1, 3, 9, 53, 67, 159, 201, 477, 603, 3551, 10653

Step-4: Factors of 31968

List of positive integer factors of 31968 that divides 31959 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 31959 and 31968. The biggest common factor number is the GCF number.
So the greatest common factor 31959 and 31968 is 9.

Also check out the Least Common Multiple of 31959 and 31968