What is the Greatest Common Factor of 37665 and 37677?

Greatest common factor (GCF) of 37665 and 37677 is 3.

GCF(37665,37677) = 3

We will now calculate the prime factors of 37665 and 37677, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37665 and 37677.

How to find the GCF of 37665 and 37677?

We will first find the prime factorization of 37665 and 37677. After we will calculate the factors of 37665 and 37677 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 37677

Prime factors of 37677 are 3, 19, 661. Prime factorization of 37677 in exponential form is:

37677 = 3¹ × 19¹ × 661¹

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 37677

List of positive integer factors of 37677 that divides 37665 without a remainder.

1, 3, 19, 57, 661, 1983, 12559

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37665 and 37677. The biggest common factor number is the GCF number.
So the greatest common factor 37665 and 37677 is 3.

Also check out the Least Common Multiple of 37665 and 37677