What is the Greatest Common Factor of 21264 and 21280?

Greatest common factor (GCF) of 21264 and 21280 is 16.

GCF(21264,21280) = 16

We will now calculate the prime factors of 21264 and 21280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21264 and 21280.

How to find the GCF of 21264 and 21280?

We will first find the prime factorization of 21264 and 21280. After we will calculate the factors of 21264 and 21280 and find the biggest common factor number .

Step-1: Prime Factorization of 21264

Prime factors of 21264 are 2, 3, 443. Prime factorization of 21264 in exponential form is:

21264 = 2⁴ × 3¹ × 443¹

Step-2: Prime Factorization of 21280

Prime factors of 21280 are 2, 5, 7, 19. Prime factorization of 21280 in exponential form is:

21280 = 2⁵ × 5¹ × 7¹ × 19¹

Step-3: Factors of 21264

List of positive integer factors of 21264 that divides 21264 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 443, 886, 1329, 1772, 2658, 3544, 5316, 7088, 10632

Step-4: Factors of 21280

List of positive integer factors of 21280 that divides 21264 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 19, 20, 28, 32, 35, 38, 40, 56, 70, 76, 80, 95, 112, 133, 140, 152, 160, 190, 224, 266, 280, 304, 380, 532, 560, 608, 665, 760, 1064, 1120, 1330, 1520, 2128, 2660, 3040, 4256, 5320, 10640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21264 and 21280. The biggest common factor number is the GCF number.
So the greatest common factor 21264 and 21280 is 16.

Also check out the Least Common Multiple of 21264 and 21280