What is the Greatest Common Factor of 22500 and 22509?

Greatest common factor (GCF) of 22500 and 22509 is 9.

GCF(22500,22509) = 9

We will now calculate the prime factors of 22500 and 22509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22500 and 22509.

How to find the GCF of 22500 and 22509?

We will first find the prime factorization of 22500 and 22509. After we will calculate the factors of 22500 and 22509 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 22509

Prime factors of 22509 are 3, 41, 61. Prime factorization of 22509 in exponential form is:

22509 = 3² × 41¹ × 61¹

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 22509

List of positive integer factors of 22509 that divides 22500 without a remainder.

1, 3, 9, 41, 61, 123, 183, 369, 549, 2501, 7503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22500 and 22509. The biggest common factor number is the GCF number.
So the greatest common factor 22500 and 22509 is 9.

Also check out the Least Common Multiple of 22500 and 22509