What is the Greatest Common Factor of 21964 and 21982?

Greatest common factor (GCF) of 21964 and 21982 is 2.

GCF(21964,21982) = 2

We will now calculate the prime factors of 21964 and 21982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21964 and 21982.

How to find the GCF of 21964 and 21982?

We will first find the prime factorization of 21964 and 21982. After we will calculate the factors of 21964 and 21982 and find the biggest common factor number .

Step-1: Prime Factorization of 21964

Prime factors of 21964 are 2, 17, 19. Prime factorization of 21964 in exponential form is:

21964 = 2² × 17² × 19¹

Step-2: Prime Factorization of 21982

Prime factors of 21982 are 2, 29, 379. Prime factorization of 21982 in exponential form is:

21982 = 2¹ × 29¹ × 379¹

Step-3: Factors of 21964

List of positive integer factors of 21964 that divides 21964 without a remainder.

1, 2, 4, 17, 19, 34, 38, 68, 76, 289, 323, 578, 646, 1156, 1292, 5491, 10982

Step-4: Factors of 21982

List of positive integer factors of 21982 that divides 21964 without a remainder.

1, 2, 29, 58, 379, 758, 10991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21964 and 21982. The biggest common factor number is the GCF number.
So the greatest common factor 21964 and 21982 is 2.

Also check out the Least Common Multiple of 21964 and 21982