What is the Greatest Common Factor of 21984 and 22000?

Greatest common factor (GCF) of 21984 and 22000 is 16.

GCF(21984,22000) = 16

We will now calculate the prime factors of 21984 and 22000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21984 and 22000.

How to find the GCF of 21984 and 22000?

We will first find the prime factorization of 21984 and 22000. After we will calculate the factors of 21984 and 22000 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 22000

Prime factors of 22000 are 2, 5, 11. Prime factorization of 22000 in exponential form is:

22000 = 2⁴ × 5³ × 11¹

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 22000

List of positive integer factors of 22000 that divides 21984 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 125, 176, 200, 220, 250, 275, 400, 440, 500, 550, 880, 1000, 1100, 1375, 2000, 2200, 2750, 4400, 5500, 11000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21984 and 22000. The biggest common factor number is the GCF number.
So the greatest common factor 21984 and 22000 is 16.

Also check out the Least Common Multiple of 21984 and 22000