What is the Greatest Common Factor of 13644 and 13659?

Greatest common factor (GCF) of 13644 and 13659 is 3.

GCF(13644,13659) = 3

We will now calculate the prime factors of 13644 and 13659, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13644 and 13659.

How to find the GCF of 13644 and 13659?

We will first find the prime factorization of 13644 and 13659. After we will calculate the factors of 13644 and 13659 and find the biggest common factor number .

Step-1: Prime Factorization of 13644

Prime factors of 13644 are 2, 3, 379. Prime factorization of 13644 in exponential form is:

13644 = 2² × 3² × 379¹

Step-2: Prime Factorization of 13659

Prime factors of 13659 are 3, 29, 157. Prime factorization of 13659 in exponential form is:

13659 = 3¹ × 29¹ × 157¹

Step-3: Factors of 13644

List of positive integer factors of 13644 that divides 13644 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 379, 758, 1137, 1516, 2274, 3411, 4548, 6822

Step-4: Factors of 13659

List of positive integer factors of 13659 that divides 13644 without a remainder.

1, 3, 29, 87, 157, 471, 4553

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13644 and 13659. The biggest common factor number is the GCF number.
So the greatest common factor 13644 and 13659 is 3.

Also check out the Least Common Multiple of 13644 and 13659