What is the Greatest Common Factor of 37968 and 37975?

Greatest common factor (GCF) of 37968 and 37975 is 7.

GCF(37968,37975) = 7

We will now calculate the prime factors of 37968 and 37975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37968 and 37975.

How to find the GCF of 37968 and 37975?

We will first find the prime factorization of 37968 and 37975. After we will calculate the factors of 37968 and 37975 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 37975

Prime factors of 37975 are 5, 7, 31. Prime factorization of 37975 in exponential form is:

37975 = 5² × 7² × 31¹

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 37975

List of positive integer factors of 37975 that divides 37968 without a remainder.

1, 5, 7, 25, 31, 35, 49, 155, 175, 217, 245, 775, 1085, 1225, 1519, 5425, 7595

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37968 and 37975. The biggest common factor number is the GCF number.
So the greatest common factor 37968 and 37975 is 7.

Also check out the Least Common Multiple of 37968 and 37975