What is the Greatest Common Factor of 1296 and 1312?

Greatest common factor (GCF) of 1296 and 1312 is 16.

GCF(1296,1312) = 16

We will now calculate the prime factors of 1296 and 1312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1296 and 1312.

How to find the GCF of 1296 and 1312?

We will first find the prime factorization of 1296 and 1312. After we will calculate the factors of 1296 and 1312 and find the biggest common factor number .

Step-1: Prime Factorization of 1296

Prime factors of 1296 are 2, 3. Prime factorization of 1296 in exponential form is:

1296 = 2⁴ × 3⁴

Step-2: Prime Factorization of 1312

Prime factors of 1312 are 2, 41. Prime factorization of 1312 in exponential form is:

1312 = 2⁵ × 41¹

Step-3: Factors of 1296

List of positive integer factors of 1296 that divides 1296 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648

Step-4: Factors of 1312

List of positive integer factors of 1312 that divides 1296 without a remainder.

1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1296 and 1312. The biggest common factor number is the GCF number.
So the greatest common factor 1296 and 1312 is 16.

Also check out the Least Common Multiple of 1296 and 1312