What is the Greatest Common Factor of 31992 and 32004?

Greatest common factor (GCF) of 31992 and 32004 is 12.

GCF(31992,32004) = 12

We will now calculate the prime factors of 31992 and 32004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31992 and 32004.

How to find the GCF of 31992 and 32004?

We will first find the prime factorization of 31992 and 32004. After we will calculate the factors of 31992 and 32004 and find the biggest common factor number .

Step-1: Prime Factorization of 31992

Prime factors of 31992 are 2, 3, 31, 43. Prime factorization of 31992 in exponential form is:

31992 = 2³ × 3¹ × 31¹ × 43¹

Step-2: Prime Factorization of 32004

Prime factors of 32004 are 2, 3, 7, 127. Prime factorization of 32004 in exponential form is:

32004 = 2² × 3² × 7¹ × 127¹

Step-3: Factors of 31992

List of positive integer factors of 31992 that divides 31992 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 31, 43, 62, 86, 93, 124, 129, 172, 186, 248, 258, 344, 372, 516, 744, 1032, 1333, 2666, 3999, 5332, 7998, 10664, 15996

Step-4: Factors of 32004

List of positive integer factors of 32004 that divides 31992 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 127, 252, 254, 381, 508, 762, 889, 1143, 1524, 1778, 2286, 2667, 3556, 4572, 5334, 8001, 10668, 16002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31992 and 32004. The biggest common factor number is the GCF number.
So the greatest common factor 31992 and 32004 is 12.

Also check out the Least Common Multiple of 31992 and 32004