What is the Greatest Common Factor of 31929 and 31944?

Greatest common factor (GCF) of 31929 and 31944 is 3.

GCF(31929,31944) = 3

We will now calculate the prime factors of 31929 and 31944, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31929 and 31944.

How to find the GCF of 31929 and 31944?

We will first find the prime factorization of 31929 and 31944. After we will calculate the factors of 31929 and 31944 and find the biggest common factor number .

Step-1: Prime Factorization of 31929

Prime factors of 31929 are 3, 29, 367. Prime factorization of 31929 in exponential form is:

31929 = 3¹ × 29¹ × 367¹

Step-2: 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-3: Factors of 31929

List of positive integer factors of 31929 that divides 31929 without a remainder.

1, 3, 29, 87, 367, 1101, 10643

Step-4: Factors of 31944

List of positive integer factors of 31944 that divides 31929 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31929 and 31944. The biggest common factor number is the GCF number.
So the greatest common factor 31929 and 31944 is 3.

Also check out the Least Common Multiple of 31929 and 31944