What is the Greatest Common Factor of 13600 and 13614?

Greatest common factor (GCF) of 13600 and 13614 is 2.

GCF(13600,13614) = 2

We will now calculate the prime factors of 13600 and 13614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13600 and 13614.

How to find the GCF of 13600 and 13614?

We will first find the prime factorization of 13600 and 13614. After we will calculate the factors of 13600 and 13614 and find the biggest common factor number .

Step-1: Prime Factorization of 13600

Prime factors of 13600 are 2, 5, 17. Prime factorization of 13600 in exponential form is:

13600 = 2⁵ × 5² × 17¹

Step-2: 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-3: Factors of 13600

List of positive integer factors of 13600 that divides 13600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 68, 80, 85, 100, 136, 160, 170, 200, 272, 340, 400, 425, 544, 680, 800, 850, 1360, 1700, 2720, 3400, 6800

Step-4: Factors of 13614

List of positive integer factors of 13614 that divides 13600 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13600 and 13614. The biggest common factor number is the GCF number.
So the greatest common factor 13600 and 13614 is 2.

Also check out the Least Common Multiple of 13600 and 13614