What is the Greatest Common Factor of 37974 and 37989?

Greatest common factor (GCF) of 37974 and 37989 is 3.

GCF(37974,37989) = 3

We will now calculate the prime factors of 37974 and 37989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37974 and 37989.

How to find the GCF of 37974 and 37989?

We will first find the prime factorization of 37974 and 37989. After we will calculate the factors of 37974 and 37989 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 37989

Prime factors of 37989 are 3, 7, 67. Prime factorization of 37989 in exponential form is:

37989 = 3⁴ × 7¹ × 67¹

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 37989

List of positive integer factors of 37989 that divides 37974 without a remainder.

1, 3, 7, 9, 21, 27, 63, 67, 81, 189, 201, 469, 567, 603, 1407, 1809, 4221, 5427, 12663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37974 and 37989. The biggest common factor number is the GCF number.
So the greatest common factor 37974 and 37989 is 3.

Also check out the Least Common Multiple of 37974 and 37989