What is the Greatest Common Factor of 10982 and 10999?

Greatest common factor (GCF) of 10982 and 10999 is 17.

GCF(10982,10999) = 17

We will now calculate the prime factors of 10982 and 10999, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10982 and 10999.

How to find the GCF of 10982 and 10999?

We will first find the prime factorization of 10982 and 10999. After we will calculate the factors of 10982 and 10999 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10999

Prime factors of 10999 are 17, 647. Prime factorization of 10999 in exponential form is:

10999 = 17¹ × 647¹

Step-3: Factors of 10982

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

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

Step-4: Factors of 10999

List of positive integer factors of 10999 that divides 10982 without a remainder.

1, 17, 647

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10982 and 10999. The biggest common factor number is the GCF number.
So the greatest common factor 10982 and 10999 is 17.

Also check out the Least Common Multiple of 10982 and 10999