What is the Greatest Common Factor of 31992 and 32007?

Greatest common factor (GCF) of 31992 and 32007 is 3.

GCF(31992,32007) = 3

We will now calculate the prime factors of 31992 and 32007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31992 and 32007.

How to find the GCF of 31992 and 32007?

We will first find the prime factorization of 31992 and 32007. After we will calculate the factors of 31992 and 32007 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 32007

Prime factors of 32007 are 3, 47, 227. Prime factorization of 32007 in exponential form is:

32007 = 3¹ × 47¹ × 227¹

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 32007

List of positive integer factors of 32007 that divides 31992 without a remainder.

1, 3, 47, 141, 227, 681, 10669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31992 and 32007. The biggest common factor number is the GCF number.
So the greatest common factor 31992 and 32007 is 3.

Also check out the Least Common Multiple of 31992 and 32007