What is the Greatest Common Factor of 31944 and 31964?

Greatest common factor (GCF) of 31944 and 31964 is 4.

GCF(31944,31964) = 4

We will now calculate the prime factors of 31944 and 31964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31944 and 31964.

How to find the GCF of 31944 and 31964?

We will first find the prime factorization of 31944 and 31964. After we will calculate the factors of 31944 and 31964 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 31964

Prime factors of 31964 are 2, 61, 131. Prime factorization of 31964 in exponential form is:

31964 = 2² × 61¹ × 131¹

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 31964

List of positive integer factors of 31964 that divides 31944 without a remainder.

1, 2, 4, 61, 122, 131, 244, 262, 524, 7991, 15982

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31944 and 31964. The biggest common factor number is the GCF number.
So the greatest common factor 31944 and 31964 is 4.

Also check out the Least Common Multiple of 31944 and 31964