What is the Greatest Common Factor of 1312 and 1322?

Greatest common factor (GCF) of 1312 and 1322 is 2.

GCF(1312,1322) = 2

We will now calculate the prime factors of 1312 and 1322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1312 and 1322.

How to find the GCF of 1312 and 1322?

We will first find the prime factorization of 1312 and 1322. After we will calculate the factors of 1312 and 1322 and find the biggest common factor number .

Step-1: Prime Factorization of 1312

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

1312 = 2⁵ × 41¹

Step-2: Prime Factorization of 1322

Prime factors of 1322 are 2, 661. Prime factorization of 1322 in exponential form is:

1322 = 2¹ × 661¹

Step-3: Factors of 1312

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

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

Step-4: Factors of 1322

List of positive integer factors of 1322 that divides 1312 without a remainder.

1, 2, 661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1312 and 1322. The biggest common factor number is the GCF number.
So the greatest common factor 1312 and 1322 is 2.

Also check out the Least Common Multiple of 1312 and 1322