What is the Greatest Common Factor of 37725 and 37737?

Greatest common factor (GCF) of 37725 and 37737 is 3.

GCF(37725,37737) = 3

We will now calculate the prime factors of 37725 and 37737, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37725 and 37737.

How to find the GCF of 37725 and 37737?

We will first find the prime factorization of 37725 and 37737. After we will calculate the factors of 37725 and 37737 and find the biggest common factor number .

Step-1: Prime Factorization of 37725

Prime factors of 37725 are 3, 5, 503. Prime factorization of 37725 in exponential form is:

37725 = 3¹ × 5² × 503¹

Step-2: Prime Factorization of 37737

Prime factors of 37737 are 3, 7, 599. Prime factorization of 37737 in exponential form is:

37737 = 3² × 7¹ × 599¹

Step-3: Factors of 37725

List of positive integer factors of 37725 that divides 37725 without a remainder.

1, 3, 5, 15, 25, 75, 503, 1509, 2515, 7545, 12575

Step-4: Factors of 37737

List of positive integer factors of 37737 that divides 37725 without a remainder.

1, 3, 7, 9, 21, 63, 599, 1797, 4193, 5391, 12579

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37725 and 37737. The biggest common factor number is the GCF number.
So the greatest common factor 37725 and 37737 is 3.

Also check out the Least Common Multiple of 37725 and 37737