What is the Greatest Common Factor of 22304 and 22320?

Greatest common factor (GCF) of 22304 and 22320 is 16.

GCF(22304,22320) = 16

We will now calculate the prime factors of 22304 and 22320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22304 and 22320.

How to find the GCF of 22304 and 22320?

We will first find the prime factorization of 22304 and 22320. After we will calculate the factors of 22304 and 22320 and find the biggest common factor number .

Step-1: Prime Factorization of 22304

Prime factors of 22304 are 2, 17, 41. Prime factorization of 22304 in exponential form is:

22304 = 2⁵ × 17¹ × 41¹

Step-2: Prime Factorization of 22320

Prime factors of 22320 are 2, 3, 5, 31. Prime factorization of 22320 in exponential form is:

22320 = 2⁴ × 3² × 5¹ × 31¹

Step-3: Factors of 22304

List of positive integer factors of 22304 that divides 22304 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 41, 68, 82, 136, 164, 272, 328, 544, 656, 697, 1312, 1394, 2788, 5576, 11152

Step-4: Factors of 22320

List of positive integer factors of 22320 that divides 22304 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 31, 36, 40, 45, 48, 60, 62, 72, 80, 90, 93, 120, 124, 144, 155, 180, 186, 240, 248, 279, 310, 360, 372, 465, 496, 558, 620, 720, 744, 930, 1116, 1240, 1395, 1488, 1860, 2232, 2480, 2790, 3720, 4464, 5580, 7440, 11160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22304 and 22320. The biggest common factor number is the GCF number.
So the greatest common factor 22304 and 22320 is 16.

Also check out the Least Common Multiple of 22304 and 22320