What is the Greatest Common Factor of 37968 and 37982?

Greatest common factor (GCF) of 37968 and 37982 is 14.

GCF(37968,37982) = 14

We will now calculate the prime factors of 37968 and 37982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37968 and 37982.

How to find the GCF of 37968 and 37982?

We will first find the prime factorization of 37968 and 37982. After we will calculate the factors of 37968 and 37982 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 37982

Prime factors of 37982 are 2, 7, 2713. Prime factorization of 37982 in exponential form is:

37982 = 2¹ × 7¹ × 2713¹

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 37982

List of positive integer factors of 37982 that divides 37968 without a remainder.

1, 2, 7, 14, 2713, 5426, 18991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37968 and 37982. The biggest common factor number is the GCF number.
So the greatest common factor 37968 and 37982 is 14.

Also check out the Least Common Multiple of 37968 and 37982