What is the Greatest Common Factor of 21600 and 21618?

Greatest common factor (GCF) of 21600 and 21618 is 18.

GCF(21600,21618) = 18

We will now calculate the prime factors of 21600 and 21618, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21600 and 21618.

How to find the GCF of 21600 and 21618?

We will first find the prime factorization of 21600 and 21618. After we will calculate the factors of 21600 and 21618 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 21618

Prime factors of 21618 are 2, 3, 1201. Prime factorization of 21618 in exponential form is:

21618 = 2¹ × 3² × 1201¹

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 21618

List of positive integer factors of 21618 that divides 21600 without a remainder.

1, 2, 3, 6, 9, 18, 1201, 2402, 3603, 7206, 10809

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21600 and 21618. The biggest common factor number is the GCF number.
So the greatest common factor 21600 and 21618 is 18.

Also check out the Least Common Multiple of 21600 and 21618