What is the Greatest Common Factor of 3657 and 3675?

Greatest common factor (GCF) of 3657 and 3675 is 3.

GCF(3657,3675) = 3

We will now calculate the prime factors of 3657 and 3675, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3657 and 3675.

How to find the GCF of 3657 and 3675?

We will first find the prime factorization of 3657 and 3675. After we will calculate the factors of 3657 and 3675 and find the biggest common factor number .

Step-1: Prime Factorization of 3657

Prime factors of 3657 are 3, 23, 53. Prime factorization of 3657 in exponential form is:

3657 = 3¹ × 23¹ × 53¹

Step-2: Prime Factorization of 3675

Prime factors of 3675 are 3, 5, 7. Prime factorization of 3675 in exponential form is:

3675 = 3¹ × 5² × 7²

Step-3: Factors of 3657

List of positive integer factors of 3657 that divides 3657 without a remainder.

1, 3, 23, 53, 69, 159, 1219

Step-4: Factors of 3675

List of positive integer factors of 3675 that divides 3657 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3657 and 3675. The biggest common factor number is the GCF number.
So the greatest common factor 3657 and 3675 is 3.

Also check out the Least Common Multiple of 3657 and 3675