What is the Greatest Common Factor of 12974 and 12980?

Greatest common factor (GCF) of 12974 and 12980 is 2.

GCF(12974,12980) = 2

We will now calculate the prime factors of 12974 and 12980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12974 and 12980.

How to find the GCF of 12974 and 12980?

We will first find the prime factorization of 12974 and 12980. After we will calculate the factors of 12974 and 12980 and find the biggest common factor number .

Step-1: Prime Factorization of 12974

Prime factors of 12974 are 2, 13, 499. Prime factorization of 12974 in exponential form is:

12974 = 2¹ × 13¹ × 499¹

Step-2: Prime Factorization of 12980

Prime factors of 12980 are 2, 5, 11, 59. Prime factorization of 12980 in exponential form is:

12980 = 2² × 5¹ × 11¹ × 59¹

Step-3: Factors of 12974

List of positive integer factors of 12974 that divides 12974 without a remainder.

1, 2, 13, 26, 499, 998, 6487

Step-4: Factors of 12980

List of positive integer factors of 12980 that divides 12974 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 59, 110, 118, 220, 236, 295, 590, 649, 1180, 1298, 2596, 3245, 6490

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12974 and 12980. The biggest common factor number is the GCF number.
So the greatest common factor 12974 and 12980 is 2.

Also check out the Least Common Multiple of 12974 and 12980