What is the Greatest Common Factor of 13296 and 13312?

Greatest common factor (GCF) of 13296 and 13312 is 16.

GCF(13296,13312) = 16

We will now calculate the prime factors of 13296 and 13312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13296 and 13312.

How to find the GCF of 13296 and 13312?

We will first find the prime factorization of 13296 and 13312. After we will calculate the factors of 13296 and 13312 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 13312

Prime factors of 13312 are 2, 13. Prime factorization of 13312 in exponential form is:

13312 = 2¹⁰ × 13¹

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 13312

List of positive integer factors of 13312 that divides 13296 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 256, 416, 512, 832, 1024, 1664, 3328, 6656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13296 and 13312. The biggest common factor number is the GCF number.
So the greatest common factor 13296 and 13312 is 16.

Also check out the Least Common Multiple of 13296 and 13312