What is the Greatest Common Factor of 37986 and 38004?

Greatest common factor (GCF) of 37986 and 38004 is 6.

GCF(37986,38004) = 6

We will now calculate the prime factors of 37986 and 38004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37986 and 38004.

How to find the GCF of 37986 and 38004?

We will first find the prime factorization of 37986 and 38004. After we will calculate the factors of 37986 and 38004 and find the biggest common factor number .

Step-1: Prime Factorization of 37986

Prime factors of 37986 are 2, 3, 13, 487. Prime factorization of 37986 in exponential form is:

37986 = 2¹ × 3¹ × 13¹ × 487¹

Step-2: Prime Factorization of 38004

Prime factors of 38004 are 2, 3, 3167. Prime factorization of 38004 in exponential form is:

38004 = 2² × 3¹ × 3167¹

Step-3: Factors of 37986

List of positive integer factors of 37986 that divides 37986 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 487, 974, 1461, 2922, 6331, 12662, 18993

Step-4: Factors of 38004

List of positive integer factors of 38004 that divides 37986 without a remainder.

1, 2, 3, 4, 6, 12, 3167, 6334, 9501, 12668, 19002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37986 and 38004. The biggest common factor number is the GCF number.
So the greatest common factor 37986 and 38004 is 6.

Also check out the Least Common Multiple of 37986 and 38004