What is the Greatest Common Factor of 21584 and 21600?

Greatest common factor (GCF) of 21584 and 21600 is 16.

GCF(21584,21600) = 16

We will now calculate the prime factors of 21584 and 21600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21584 and 21600.

How to find the GCF of 21584 and 21600?

We will first find the prime factorization of 21584 and 21600. After we will calculate the factors of 21584 and 21600 and find the biggest common factor number .

Step-1: Prime Factorization of 21584

Prime factors of 21584 are 2, 19, 71. Prime factorization of 21584 in exponential form is:

21584 = 2⁴ × 19¹ × 71¹

Step-2: 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-3: Factors of 21584

List of positive integer factors of 21584 that divides 21584 without a remainder.

1, 2, 4, 8, 16, 19, 38, 71, 76, 142, 152, 284, 304, 568, 1136, 1349, 2698, 5396, 10792

Step-4: Factors of 21600

List of positive integer factors of 21600 that divides 21584 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21584 and 21600. The biggest common factor number is the GCF number.
So the greatest common factor 21584 and 21600 is 16.

Also check out the Least Common Multiple of 21584 and 21600