What is the Greatest Common Factor of 10974 and 10982?

Greatest common factor (GCF) of 10974 and 10982 is 2.

GCF(10974,10982) = 2

We will now calculate the prime factors of 10974 and 10982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10974 and 10982.

How to find the GCF of 10974 and 10982?

We will first find the prime factorization of 10974 and 10982. After we will calculate the factors of 10974 and 10982 and find the biggest common factor number .

Step-1: Prime Factorization of 10974

Prime factors of 10974 are 2, 3, 31, 59. Prime factorization of 10974 in exponential form is:

10974 = 2¹ × 3¹ × 31¹ × 59¹

Step-2: Prime Factorization of 10982

Prime factors of 10982 are 2, 17, 19. Prime factorization of 10982 in exponential form is:

10982 = 2¹ × 17² × 19¹

Step-3: Factors of 10974

List of positive integer factors of 10974 that divides 10974 without a remainder.

1, 2, 3, 6, 31, 59, 62, 93, 118, 177, 186, 354, 1829, 3658, 5487

Step-4: Factors of 10982

List of positive integer factors of 10982 that divides 10974 without a remainder.

1, 2, 17, 19, 34, 38, 289, 323, 578, 646, 5491

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10974 and 10982. The biggest common factor number is the GCF number.
So the greatest common factor 10974 and 10982 is 2.

Also check out the Least Common Multiple of 10974 and 10982