What is the Greatest Common Factor of 13296 and 13314?

Greatest common factor (GCF) of 13296 and 13314 is 6.

GCF(13296,13314) = 6

We will now calculate the prime factors of 13296 and 13314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13296 and 13314.

How to find the GCF of 13296 and 13314?

We will first find the prime factorization of 13296 and 13314. After we will calculate the factors of 13296 and 13314 and find the biggest common factor number .

Step-1: Prime Factorization of 13296

Prime factors of 13296 are 2, 3, 277. Prime factorization of 13296 in exponential form is:

13296 = 2⁴ × 3¹ × 277¹

Step-2: Prime Factorization of 13314

Prime factors of 13314 are 2, 3, 7, 317. Prime factorization of 13314 in exponential form is:

13314 = 2¹ × 3¹ × 7¹ × 317¹

Step-3: Factors of 13296

List of positive integer factors of 13296 that divides 13296 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 277, 554, 831, 1108, 1662, 2216, 3324, 4432, 6648

Step-4: Factors of 13314

List of positive integer factors of 13314 that divides 13296 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 317, 634, 951, 1902, 2219, 4438, 6657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13296 and 13314. The biggest common factor number is the GCF number.
So the greatest common factor 13296 and 13314 is 6.

Also check out the Least Common Multiple of 13296 and 13314