What is the Greatest Common Factor of 21744 and 21760?

Greatest common factor (GCF) of 21744 and 21760 is 16.

GCF(21744,21760) = 16

We will now calculate the prime factors of 21744 and 21760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21744 and 21760.

How to find the GCF of 21744 and 21760?

We will first find the prime factorization of 21744 and 21760. After we will calculate the factors of 21744 and 21760 and find the biggest common factor number .

Step-1: Prime Factorization of 21744

Prime factors of 21744 are 2, 3, 151. Prime factorization of 21744 in exponential form is:

21744 = 2⁴ × 3² × 151¹

Step-2: Prime Factorization of 21760

Prime factors of 21760 are 2, 5, 17. Prime factorization of 21760 in exponential form is:

21760 = 2⁸ × 5¹ × 17¹

Step-3: Factors of 21744

List of positive integer factors of 21744 that divides 21744 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 151, 302, 453, 604, 906, 1208, 1359, 1812, 2416, 2718, 3624, 5436, 7248, 10872

Step-4: Factors of 21760

List of positive integer factors of 21760 that divides 21744 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 128, 136, 160, 170, 256, 272, 320, 340, 544, 640, 680, 1088, 1280, 1360, 2176, 2720, 4352, 5440, 10880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21744 and 21760. The biggest common factor number is the GCF number.
So the greatest common factor 21744 and 21760 is 16.

Also check out the Least Common Multiple of 21744 and 21760