What is the Greatest Common Factor of 13614 and 13629?

Greatest common factor (GCF) of 13614 and 13629 is 3.

GCF(13614,13629) = 3

We will now calculate the prime factors of 13614 and 13629, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13614 and 13629.

How to find the GCF of 13614 and 13629?

We will first find the prime factorization of 13614 and 13629. After we will calculate the factors of 13614 and 13629 and find the biggest common factor number .

Step-1: Prime Factorization of 13614

Prime factors of 13614 are 2, 3, 2269. Prime factorization of 13614 in exponential form is:

13614 = 2¹ × 3¹ × 2269¹

Step-2: Prime Factorization of 13629

Prime factors of 13629 are 3, 7, 11, 59. Prime factorization of 13629 in exponential form is:

13629 = 3¹ × 7¹ × 11¹ × 59¹

Step-3: Factors of 13614

List of positive integer factors of 13614 that divides 13614 without a remainder.

1, 2, 3, 6, 2269, 4538, 6807

Step-4: Factors of 13629

List of positive integer factors of 13629 that divides 13614 without a remainder.

1, 3, 7, 11, 21, 33, 59, 77, 177, 231, 413, 649, 1239, 1947, 4543

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13614 and 13629. The biggest common factor number is the GCF number.
So the greatest common factor 13614 and 13629 is 3.

Also check out the Least Common Multiple of 13614 and 13629