What is the Greatest Common Factor of 3645 and 3657?

Greatest common factor (GCF) of 3645 and 3657 is 3.

GCF(3645,3657) = 3

We will now calculate the prime factors of 3645 and 3657, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3645 and 3657.

How to find the GCF of 3645 and 3657?

We will first find the prime factorization of 3645 and 3657. After we will calculate the factors of 3645 and 3657 and find the biggest common factor number .

Step-1: Prime Factorization of 3645

Prime factors of 3645 are 3, 5. Prime factorization of 3645 in exponential form is:

3645 = 3⁶ × 5¹

Step-2: 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-3: Factors of 3645

List of positive integer factors of 3645 that divides 3645 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 729, 1215

Step-4: Factors of 3657

List of positive integer factors of 3657 that divides 3645 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3645 and 3657. The biggest common factor number is the GCF number.
So the greatest common factor 3645 and 3657 is 3.

Also check out the Least Common Multiple of 3645 and 3657