What is the Greatest Common Factor of 22500 and 22518?

Greatest common factor (GCF) of 22500 and 22518 is 18.

GCF(22500,22518) = 18

We will now calculate the prime factors of 22500 and 22518, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22500 and 22518.

How to find the GCF of 22500 and 22518?

We will first find the prime factorization of 22500 and 22518. After we will calculate the factors of 22500 and 22518 and find the biggest common factor number .

Step-1: Prime Factorization of 22500

Prime factors of 22500 are 2, 3, 5. Prime factorization of 22500 in exponential form is:

22500 = 2² × 3² × 5⁴

Step-2: Prime Factorization of 22518

Prime factors of 22518 are 2, 3, 139. Prime factorization of 22518 in exponential form is:

22518 = 2¹ × 3⁴ × 139¹

Step-3: Factors of 22500

List of positive integer factors of 22500 that divides 22500 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 625, 750, 900, 1125, 1250, 1500, 1875, 2250, 2500, 3750, 4500, 5625, 7500, 11250

Step-4: Factors of 22518

List of positive integer factors of 22518 that divides 22500 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 139, 162, 278, 417, 834, 1251, 2502, 3753, 7506, 11259

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22500 and 22518. The biggest common factor number is the GCF number.
So the greatest common factor 22500 and 22518 is 18.

Also check out the Least Common Multiple of 22500 and 22518