What is the Greatest Common Factor of 21600 and 21616?

Greatest common factor (GCF) of 21600 and 21616 is 16.

GCF(21600,21616) = 16

We will now calculate the prime factors of 21600 and 21616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21600 and 21616.

How to find the GCF of 21600 and 21616?

We will first find the prime factorization of 21600 and 21616. After we will calculate the factors of 21600 and 21616 and find the biggest common factor number .

Step-1: Prime Factorization of 21600

Prime factors of 21600 are 2, 3, 5. Prime factorization of 21600 in exponential form is:

21600 = 2⁵ × 3³ × 5²

Step-2: Prime Factorization of 21616

Prime factors of 21616 are 2, 7, 193. Prime factorization of 21616 in exponential form is:

21616 = 2⁴ × 7¹ × 193¹

Step-3: Factors of 21600

List of positive integer factors of 21600 that divides 21600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 96, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 675, 720, 800, 864, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2400, 2700, 3600, 4320, 5400, 7200, 10800

Step-4: Factors of 21616

List of positive integer factors of 21616 that divides 21600 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 193, 386, 772, 1351, 1544, 2702, 3088, 5404, 10808

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21600 and 21616. The biggest common factor number is the GCF number.
So the greatest common factor 21600 and 21616 is 16.

Also check out the Least Common Multiple of 21600 and 21616