What is the Greatest Common Factor of 1298 and 1312?

Greatest common factor (GCF) of 1298 and 1312 is 2.

GCF(1298,1312) = 2

We will now calculate the prime factors of 1298 and 1312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1298 and 1312.

How to find the GCF of 1298 and 1312?

We will first find the prime factorization of 1298 and 1312. After we will calculate the factors of 1298 and 1312 and find the biggest common factor number .

Step-1: Prime Factorization of 1298

Prime factors of 1298 are 2, 11, 59. Prime factorization of 1298 in exponential form is:

1298 = 2¹ × 11¹ × 59¹

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 1298

List of positive integer factors of 1298 that divides 1298 without a remainder.

1, 2, 11, 22, 59, 118, 649

Step-4: Factors of 1312

List of positive integer factors of 1312 that divides 1298 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 1298 and 1312. The biggest common factor number is the GCF number.
So the greatest common factor 1298 and 1312 is 2.

Also check out the Least Common Multiple of 1298 and 1312