What is the Greatest Common Factor of 37974 and 37980?

Greatest common factor (GCF) of 37974 and 37980 is 6.

GCF(37974,37980) = 6

We will now calculate the prime factors of 37974 and 37980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37974 and 37980.

How to find the GCF of 37974 and 37980?

We will first find the prime factorization of 37974 and 37980. After we will calculate the factors of 37974 and 37980 and find the biggest common factor number .

Step-1: Prime Factorization of 37974

Prime factors of 37974 are 2, 3, 6329. Prime factorization of 37974 in exponential form is:

37974 = 2¹ × 3¹ × 6329¹

Step-2: 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-3: Factors of 37974

List of positive integer factors of 37974 that divides 37974 without a remainder.

1, 2, 3, 6, 6329, 12658, 18987

Step-4: Factors of 37980

List of positive integer factors of 37980 that divides 37974 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37974 and 37980. The biggest common factor number is the GCF number.
So the greatest common factor 37974 and 37980 is 6.

Also check out the Least Common Multiple of 37974 and 37980