What is the Greatest Common Factor of 21971 and 21984?

Greatest common factor (GCF) of 21971 and 21984 is 1.

GCF(21971,21984) = 1

We will now calculate the prime factors of 21971 and 21984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21971 and 21984.

How to find the GCF of 21971 and 21984?

We will first find the prime factorization of 21971 and 21984. After we will calculate the factors of 21971 and 21984 and find the biggest common factor number .

Step-1: Prime Factorization of 21971

Prime factors of 21971 are 127, 173. Prime factorization of 21971 in exponential form is:

21971 = 127¹ × 173¹

Step-2: 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-3: Factors of 21971

List of positive integer factors of 21971 that divides 21971 without a remainder.

1, 127, 173

Step-4: Factors of 21984

List of positive integer factors of 21984 that divides 21971 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21971 and 21984. The biggest common factor number is the GCF number.
So the greatest common factor 21971 and 21984 is 1.

Also check out the Least Common Multiple of 21971 and 21984