What is the Greatest Common Factor of 3648 and 3657?

Greatest common factor (GCF) of 3648 and 3657 is 3.

GCF(3648,3657) = 3

We will now calculate the prime factors of 3648 and 3657, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3648 and 3657.

How to find the GCF of 3648 and 3657?

We will first find the prime factorization of 3648 and 3657. After we will calculate the factors of 3648 and 3657 and find the biggest common factor number .

Step-1: Prime Factorization of 3648

Prime factors of 3648 are 2, 3, 19. Prime factorization of 3648 in exponential form is:

3648 = 2⁶ × 3¹ × 19¹

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 3648

List of positive integer factors of 3648 that divides 3648 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 152, 192, 228, 304, 456, 608, 912, 1216, 1824

Step-4: Factors of 3657

List of positive integer factors of 3657 that divides 3648 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3648 and 3657. The biggest common factor number is the GCF number.
So the greatest common factor 3648 and 3657 is 3.

Also check out the Least Common Multiple of 3648 and 3657