What is the Greatest Common Factor of 21440 and 21456?

Greatest common factor (GCF) of 21440 and 21456 is 16.

GCF(21440,21456) = 16

We will now calculate the prime factors of 21440 and 21456, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21440 and 21456.

How to find the GCF of 21440 and 21456?

We will first find the prime factorization of 21440 and 21456. After we will calculate the factors of 21440 and 21456 and find the biggest common factor number .

Step-1: Prime Factorization of 21440

Prime factors of 21440 are 2, 5, 67. Prime factorization of 21440 in exponential form is:

21440 = 2⁶ × 5¹ × 67¹

Step-2: Prime Factorization of 21456

Prime factors of 21456 are 2, 3, 149. Prime factorization of 21456 in exponential form is:

21456 = 2⁴ × 3² × 149¹

Step-3: Factors of 21440

List of positive integer factors of 21440 that divides 21440 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 67, 80, 134, 160, 268, 320, 335, 536, 670, 1072, 1340, 2144, 2680, 4288, 5360, 10720

Step-4: Factors of 21456

List of positive integer factors of 21456 that divides 21440 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 149, 298, 447, 596, 894, 1192, 1341, 1788, 2384, 2682, 3576, 5364, 7152, 10728

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21440 and 21456. The biggest common factor number is the GCF number.
So the greatest common factor 21440 and 21456 is 16.

Also check out the Least Common Multiple of 21440 and 21456