What is the Greatest Common Factor of 37968 and 37974?

Greatest common factor (GCF) of 37968 and 37974 is 6.

GCF(37968,37974) = 6

We will now calculate the prime factors of 37968 and 37974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37968 and 37974.

How to find the GCF of 37968 and 37974?

We will first find the prime factorization of 37968 and 37974. After we will calculate the factors of 37968 and 37974 and find the biggest common factor number .

Step-1: Prime Factorization of 37968

Prime factors of 37968 are 2, 3, 7, 113. Prime factorization of 37968 in exponential form is:

37968 = 2⁴ × 3¹ × 7¹ × 113¹

Step-2: 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-3: Factors of 37968

List of positive integer factors of 37968 that divides 37968 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 113, 168, 226, 336, 339, 452, 678, 791, 904, 1356, 1582, 1808, 2373, 2712, 3164, 4746, 5424, 6328, 9492, 12656, 18984

Step-4: Factors of 37974

List of positive integer factors of 37974 that divides 37968 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37968 and 37974. The biggest common factor number is the GCF number.
So the greatest common factor 37968 and 37974 is 6.

Also check out the Least Common Multiple of 37968 and 37974