What is the Greatest Common Factor of 13614 and 13624?

Greatest common factor (GCF) of 13614 and 13624 is 2.

GCF(13614,13624) = 2

We will now calculate the prime factors of 13614 and 13624, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13614 and 13624.

How to find the GCF of 13614 and 13624?

We will first find the prime factorization of 13614 and 13624. After we will calculate the factors of 13614 and 13624 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 13624

Prime factors of 13624 are 2, 13, 131. Prime factorization of 13624 in exponential form is:

13624 = 2³ × 13¹ × 131¹

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 13624

List of positive integer factors of 13624 that divides 13614 without a remainder.

1, 2, 4, 8, 13, 26, 52, 104, 131, 262, 524, 1048, 1703, 3406, 6812

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13614 and 13624. The biggest common factor number is the GCF number.
So the greatest common factor 13614 and 13624 is 2.

Also check out the Least Common Multiple of 13614 and 13624