What is the Greatest Common Factor of 3657 and 3672?

Greatest common factor (GCF) of 3657 and 3672 is 3.

GCF(3657,3672) = 3

We will now calculate the prime factors of 3657 and 3672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3657 and 3672.

How to find the GCF of 3657 and 3672?

We will first find the prime factorization of 3657 and 3672. After we will calculate the factors of 3657 and 3672 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 3672

Prime factors of 3672 are 2, 3, 17. Prime factorization of 3672 in exponential form is:

3672 = 2³ × 3³ × 17¹

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 3672

List of positive integer factors of 3672 that divides 3657 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 27, 34, 36, 51, 54, 68, 72, 102, 108, 136, 153, 204, 216, 306, 408, 459, 612, 918, 1224, 1836

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3657 and 3672. The biggest common factor number is the GCF number.
So the greatest common factor 3657 and 3672 is 3.

Also check out the Least Common Multiple of 3657 and 3672