What is the Greatest Common Factor of 37980 and 37986?

Greatest common factor (GCF) of 37980 and 37986 is 6.

GCF(37980,37986) = 6

We will now calculate the prime factors of 37980 and 37986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37980 and 37986.

How to find the GCF of 37980 and 37986?

We will first find the prime factorization of 37980 and 37986. After we will calculate the factors of 37980 and 37986 and find the biggest common factor number .

Step-1: Prime Factorization of 37980

Prime factors of 37980 are 2, 3, 5, 211. Prime factorization of 37980 in exponential form is:

37980 = 2² × 3² × 5¹ × 211¹

Step-2: 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-3: Factors of 37980

List of positive integer factors of 37980 that divides 37980 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 211, 422, 633, 844, 1055, 1266, 1899, 2110, 2532, 3165, 3798, 4220, 6330, 7596, 9495, 12660, 18990

Step-4: Factors of 37986

List of positive integer factors of 37986 that divides 37980 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37980 and 37986. The biggest common factor number is the GCF number.
So the greatest common factor 37980 and 37986 is 6.

Also check out the Least Common Multiple of 37980 and 37986