What is the Greatest Common Factor of 13635 and 13644?

Greatest common factor (GCF) of 13635 and 13644 is 9.

GCF(13635,13644) = 9

We will now calculate the prime factors of 13635 and 13644, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13635 and 13644.

How to find the GCF of 13635 and 13644?

We will first find the prime factorization of 13635 and 13644. After we will calculate the factors of 13635 and 13644 and find the biggest common factor number .

Step-1: Prime Factorization of 13635

Prime factors of 13635 are 3, 5, 101. Prime factorization of 13635 in exponential form is:

13635 = 3³ × 5¹ × 101¹

Step-2: 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-3: Factors of 13635

List of positive integer factors of 13635 that divides 13635 without a remainder.

1, 3, 5, 9, 15, 27, 45, 101, 135, 303, 505, 909, 1515, 2727, 4545

Step-4: Factors of 13644

List of positive integer factors of 13644 that divides 13635 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13635 and 13644. The biggest common factor number is the GCF number.
So the greatest common factor 13635 and 13644 is 9.

Also check out the Least Common Multiple of 13635 and 13644