What is the Greatest Common Factor of 37665 and 37675?

Greatest common factor (GCF) of 37665 and 37675 is 5.

GCF(37665,37675) = 5

We will now calculate the prime factors of 37665 and 37675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37665 and 37675.

How to find the GCF of 37665 and 37675?

We will first find the prime factorization of 37665 and 37675. After we will calculate the factors of 37665 and 37675 and find the biggest common factor number .

Step-1: Prime Factorization of 37665

Prime factors of 37665 are 3, 5, 31. Prime factorization of 37665 in exponential form is:

37665 = 3⁵ × 5¹ × 31¹

Step-2: Prime Factorization of 37675

Prime factors of 37675 are 5, 11, 137. Prime factorization of 37675 in exponential form is:

37675 = 5² × 11¹ × 137¹

Step-3: Factors of 37665

List of positive integer factors of 37665 that divides 37665 without a remainder.

1, 3, 5, 9, 15, 27, 31, 45, 81, 93, 135, 155, 243, 279, 405, 465, 837, 1215, 1395, 2511, 4185, 7533, 12555

Step-4: Factors of 37675

List of positive integer factors of 37675 that divides 37665 without a remainder.

1, 5, 11, 25, 55, 137, 275, 685, 1507, 3425, 7535

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37665 and 37675. The biggest common factor number is the GCF number.
So the greatest common factor 37665 and 37675 is 5.

Also check out the Least Common Multiple of 37665 and 37675