What is the Greatest Common Factor of 3614 and 3627?

Greatest common factor (GCF) of 3614 and 3627 is 13.

GCF(3614,3627) = 13

We will now calculate the prime factors of 3614 and 3627, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3614 and 3627.

How to find the GCF of 3614 and 3627?

We will first find the prime factorization of 3614 and 3627. After we will calculate the factors of 3614 and 3627 and find the biggest common factor number .

Step-1: Prime Factorization of 3614

Prime factors of 3614 are 2, 13, 139. Prime factorization of 3614 in exponential form is:

3614 = 2¹ × 13¹ × 139¹

Step-2: Prime Factorization of 3627

Prime factors of 3627 are 3, 13, 31. Prime factorization of 3627 in exponential form is:

3627 = 3² × 13¹ × 31¹

Step-3: Factors of 3614

List of positive integer factors of 3614 that divides 3614 without a remainder.

1, 2, 13, 26, 139, 278, 1807

Step-4: Factors of 3627

List of positive integer factors of 3627 that divides 3614 without a remainder.

1, 3, 9, 13, 31, 39, 93, 117, 279, 403, 1209

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3614 and 3627. The biggest common factor number is the GCF number.
So the greatest common factor 3614 and 3627 is 13.

Also check out the Least Common Multiple of 3614 and 3627