What is the Greatest Common Factor of 21984 and 21999?

Greatest common factor (GCF) of 21984 and 21999 is 3.

GCF(21984,21999) = 3

We will now calculate the prime factors of 21984 and 21999, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21984 and 21999.

How to find the GCF of 21984 and 21999?

We will first find the prime factorization of 21984 and 21999. After we will calculate the factors of 21984 and 21999 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 21999

Prime factors of 21999 are 3, 7333. Prime factorization of 21999 in exponential form is:

21999 = 3¹ × 7333¹

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 21999

List of positive integer factors of 21999 that divides 21984 without a remainder.

1, 3, 7333

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21984 and 21999. The biggest common factor number is the GCF number.
So the greatest common factor 21984 and 21999 is 3.

Also check out the Least Common Multiple of 21984 and 21999