What is the Greatest Common Factor of 13608 and 13614?

Greatest common factor (GCF) of 13608 and 13614 is 6.

GCF(13608,13614) = 6

We will now calculate the prime factors of 13608 and 13614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13608 and 13614.

How to find the GCF of 13608 and 13614?

We will first find the prime factorization of 13608 and 13614. After we will calculate the factors of 13608 and 13614 and find the biggest common factor number .

Step-1: Prime Factorization of 13608

Prime factors of 13608 are 2, 3, 7. Prime factorization of 13608 in exponential form is:

13608 = 2³ × 3⁵ × 7¹

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 13608

List of positive integer factors of 13608 that divides 13608 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 81, 84, 108, 126, 162, 168, 189, 216, 243, 252, 324, 378, 486, 504, 567, 648, 756, 972, 1134, 1512, 1701, 1944, 2268, 3402, 4536, 6804

Step-4: Factors of 13614

List of positive integer factors of 13614 that divides 13608 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13608 and 13614. The biggest common factor number is the GCF number.
So the greatest common factor 13608 and 13614 is 6.

Also check out the Least Common Multiple of 13608 and 13614