What is the Greatest Common Factor of 31944 and 31959?

Greatest common factor (GCF) of 31944 and 31959 is 3.

GCF(31944,31959) = 3

We will now calculate the prime factors of 31944 and 31959, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31944 and 31959.

How to find the GCF of 31944 and 31959?

We will first find the prime factorization of 31944 and 31959. After we will calculate the factors of 31944 and 31959 and find the biggest common factor number .

Step-1: Prime Factorization of 31944

Prime factors of 31944 are 2, 3, 11. Prime factorization of 31944 in exponential form is:

31944 = 2³ × 3¹ × 11³

Step-2: 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-3: Factors of 31944

List of positive integer factors of 31944 that divides 31944 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 121, 132, 242, 264, 363, 484, 726, 968, 1331, 1452, 2662, 2904, 3993, 5324, 7986, 10648, 15972

Step-4: Factors of 31959

List of positive integer factors of 31959 that divides 31944 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31944 and 31959. The biggest common factor number is the GCF number.
So the greatest common factor 31944 and 31959 is 3.

Also check out the Least Common Multiple of 31944 and 31959