What is the Greatest Common Factor of 21964 and 21972?

Greatest common factor (GCF) of 21964 and 21972 is 4.

GCF(21964,21972) = 4

We will now calculate the prime factors of 21964 and 21972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21964 and 21972.

How to find the GCF of 21964 and 21972?

We will first find the prime factorization of 21964 and 21972. After we will calculate the factors of 21964 and 21972 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 21972

Prime factors of 21972 are 2, 3, 1831. Prime factorization of 21972 in exponential form is:

21972 = 2² × 3¹ × 1831¹

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 21972

List of positive integer factors of 21972 that divides 21964 without a remainder.

1, 2, 3, 4, 6, 12, 1831, 3662, 5493, 7324, 10986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21964 and 21972. The biggest common factor number is the GCF number.
So the greatest common factor 21964 and 21972 is 4.

Also check out the Least Common Multiple of 21964 and 21972