What is the Greatest Common Factor of 21296 and 21312?

Greatest common factor (GCF) of 21296 and 21312 is 16.

GCF(21296,21312) = 16

We will now calculate the prime factors of 21296 and 21312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21296 and 21312.

How to find the GCF of 21296 and 21312?

We will first find the prime factorization of 21296 and 21312. After we will calculate the factors of 21296 and 21312 and find the biggest common factor number .

Step-1: Prime Factorization of 21296

Prime factors of 21296 are 2, 11. Prime factorization of 21296 in exponential form is:

21296 = 2⁴ × 11³

Step-2: Prime Factorization of 21312

Prime factors of 21312 are 2, 3, 37. Prime factorization of 21312 in exponential form is:

21312 = 2⁶ × 3² × 37¹

Step-3: Factors of 21296

List of positive integer factors of 21296 that divides 21296 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 121, 176, 242, 484, 968, 1331, 1936, 2662, 5324, 10648

Step-4: Factors of 21312

List of positive integer factors of 21312 that divides 21296 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 37, 48, 64, 72, 74, 96, 111, 144, 148, 192, 222, 288, 296, 333, 444, 576, 592, 666, 888, 1184, 1332, 1776, 2368, 2664, 3552, 5328, 7104, 10656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21296 and 21312. The biggest common factor number is the GCF number.
So the greatest common factor 21296 and 21312 is 16.

Also check out the Least Common Multiple of 21296 and 21312