What is the Greatest Common Factor of 31944 and 31950?

Greatest common factor (GCF) of 31944 and 31950 is 6.

GCF(31944,31950) = 6

We will now calculate the prime factors of 31944 and 31950, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31944 and 31950.

How to find the GCF of 31944 and 31950?

We will first find the prime factorization of 31944 and 31950. After we will calculate the factors of 31944 and 31950 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 31950

Prime factors of 31950 are 2, 3, 5, 71. Prime factorization of 31950 in exponential form is:

31950 = 2¹ × 3² × 5² × 71¹

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 31950

List of positive integer factors of 31950 that divides 31944 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 71, 75, 90, 142, 150, 213, 225, 355, 426, 450, 639, 710, 1065, 1278, 1775, 2130, 3195, 3550, 5325, 6390, 10650, 15975

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31944 and 31950. The biggest common factor number is the GCF number.
So the greatest common factor 31944 and 31950 is 6.

Also check out the Least Common Multiple of 31944 and 31950