What is the Greatest Common Factor of 21984 and 22004?

Greatest common factor (GCF) of 21984 and 22004 is 4.

GCF(21984,22004) = 4

We will now calculate the prime factors of 21984 and 22004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21984 and 22004.

How to find the GCF of 21984 and 22004?

We will first find the prime factorization of 21984 and 22004. After we will calculate the factors of 21984 and 22004 and find the biggest common factor number .

Step-1: Prime Factorization of 21984

Prime factors of 21984 are 2, 3, 229. Prime factorization of 21984 in exponential form is:

21984 = 2⁵ × 3¹ × 229¹

Step-2: Prime Factorization of 22004

Prime factors of 22004 are 2, 5501. Prime factorization of 22004 in exponential form is:

22004 = 2² × 5501¹

Step-3: Factors of 21984

List of positive integer factors of 21984 that divides 21984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 229, 458, 687, 916, 1374, 1832, 2748, 3664, 5496, 7328, 10992

Step-4: Factors of 22004

List of positive integer factors of 22004 that divides 21984 without a remainder.

1, 2, 4, 5501, 11002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21984 and 22004. The biggest common factor number is the GCF number.
So the greatest common factor 21984 and 22004 is 4.

Also check out the Least Common Multiple of 21984 and 22004