What is the Greatest Common Factor of 31984 and 32004?

Greatest common factor (GCF) of 31984 and 32004 is 4.

GCF(31984,32004) = 4

We will now calculate the prime factors of 31984 and 32004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31984 and 32004.

How to find the GCF of 31984 and 32004?

We will first find the prime factorization of 31984 and 32004. After we will calculate the factors of 31984 and 32004 and find the biggest common factor number .

Step-1: Prime Factorization of 31984

Prime factors of 31984 are 2, 1999. Prime factorization of 31984 in exponential form is:

31984 = 2⁴ × 1999¹

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 31984

List of positive integer factors of 31984 that divides 31984 without a remainder.

1, 2, 4, 8, 16, 1999, 3998, 7996, 15992

Step-4: Factors of 32004

List of positive integer factors of 32004 that divides 31984 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 31984 and 32004. The biggest common factor number is the GCF number.
So the greatest common factor 31984 and 32004 is 4.

Also check out the Least Common Multiple of 31984 and 32004