What is the Greatest Common Factor of 31944 and 31962?

Greatest common factor (GCF) of 31944 and 31962 is 6.

GCF(31944,31962) = 6

We will now calculate the prime factors of 31944 and 31962, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31944 and 31962.

How to find the GCF of 31944 and 31962?

We will first find the prime factorization of 31944 and 31962. After we will calculate the factors of 31944 and 31962 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 31962

Prime factors of 31962 are 2, 3, 7, 761. Prime factorization of 31962 in exponential form is:

31962 = 2¹ × 3¹ × 7¹ × 761¹

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 31962

List of positive integer factors of 31962 that divides 31944 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 761, 1522, 2283, 4566, 5327, 10654, 15981

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31944 and 31962. The biggest common factor number is the GCF number.
So the greatest common factor 31944 and 31962 is 6.

Also check out the Least Common Multiple of 31944 and 31962