What is the Greatest Common Factor of 21600 and 21615?

Greatest common factor (GCF) of 21600 and 21615 is 15.

GCF(21600,21615) = 15

We will now calculate the prime factors of 21600 and 21615, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21600 and 21615.

How to find the GCF of 21600 and 21615?

We will first find the prime factorization of 21600 and 21615. After we will calculate the factors of 21600 and 21615 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 21615

Prime factors of 21615 are 3, 5, 11, 131. Prime factorization of 21615 in exponential form is:

21615 = 3¹ × 5¹ × 11¹ × 131¹

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 21615

List of positive integer factors of 21615 that divides 21600 without a remainder.

1, 3, 5, 11, 15, 33, 55, 131, 165, 393, 655, 1441, 1965, 4323, 7205

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21600 and 21615. The biggest common factor number is the GCF number.
So the greatest common factor 21600 and 21615 is 15.

Also check out the Least Common Multiple of 21600 and 21615