What is the Greatest Common Factor of 21984 and 21989?

Greatest common factor (GCF) of 21984 and 21989 is 1.

GCF(21984,21989) = 1

We will now calculate the prime factors of 21984 and 21989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21984 and 21989.

How to find the GCF of 21984 and 21989?

We will first find the prime factorization of 21984 and 21989. After we will calculate the factors of 21984 and 21989 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 21989

Prime factors of 21989 are 11, 1999. Prime factorization of 21989 in exponential form is:

21989 = 11¹ × 1999¹

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 21989

List of positive integer factors of 21989 that divides 21984 without a remainder.

1, 11, 1999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21984 and 21989. The biggest common factor number is the GCF number.
So the greatest common factor 21984 and 21989 is 1.

Also check out the Least Common Multiple of 21984 and 21989