What is the Greatest Common Factor of 21586 and 21600?

Greatest common factor (GCF) of 21586 and 21600 is 2.

GCF(21586,21600) = 2

We will now calculate the prime factors of 21586 and 21600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21586 and 21600.

How to find the GCF of 21586 and 21600?

We will first find the prime factorization of 21586 and 21600. After we will calculate the factors of 21586 and 21600 and find the biggest common factor number .

Step-1: Prime Factorization of 21586

Prime factors of 21586 are 2, 43, 251. Prime factorization of 21586 in exponential form is:

21586 = 2¹ × 43¹ × 251¹

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 21586

List of positive integer factors of 21586 that divides 21586 without a remainder.

1, 2, 43, 86, 251, 502, 10793

Step-4: Factors of 21600

List of positive integer factors of 21600 that divides 21586 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 21586 and 21600. The biggest common factor number is the GCF number.
So the greatest common factor 21586 and 21600 is 2.

Also check out the Least Common Multiple of 21586 and 21600