What is the Greatest Common Factor of 21648 and 21664?

Greatest common factor (GCF) of 21648 and 21664 is 16.

GCF(21648,21664) = 16

We will now calculate the prime factors of 21648 and 21664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21648 and 21664.

How to find the GCF of 21648 and 21664?

We will first find the prime factorization of 21648 and 21664. After we will calculate the factors of 21648 and 21664 and find the biggest common factor number .

Step-1: Prime Factorization of 21648

Prime factors of 21648 are 2, 3, 11, 41. Prime factorization of 21648 in exponential form is:

21648 = 2⁴ × 3¹ × 11¹ × 41¹

Step-2: Prime Factorization of 21664

Prime factors of 21664 are 2, 677. Prime factorization of 21664 in exponential form is:

21664 = 2⁵ × 677¹

Step-3: Factors of 21648

List of positive integer factors of 21648 that divides 21648 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 41, 44, 48, 66, 82, 88, 123, 132, 164, 176, 246, 264, 328, 451, 492, 528, 656, 902, 984, 1353, 1804, 1968, 2706, 3608, 5412, 7216, 10824

Step-4: Factors of 21664

List of positive integer factors of 21664 that divides 21648 without a remainder.

1, 2, 4, 8, 16, 32, 677, 1354, 2708, 5416, 10832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21648 and 21664. The biggest common factor number is the GCF number.
So the greatest common factor 21648 and 21664 is 16.

Also check out the Least Common Multiple of 21648 and 21664