What is the Greatest Common Factor of 22500 and 22514?

Greatest common factor (GCF) of 22500 and 22514 is 2.

GCF(22500,22514) = 2

We will now calculate the prime factors of 22500 and 22514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22500 and 22514.

How to find the GCF of 22500 and 22514?

We will first find the prime factorization of 22500 and 22514. After we will calculate the factors of 22500 and 22514 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 22514

Prime factors of 22514 are 2, 11257. Prime factorization of 22514 in exponential form is:

22514 = 2¹ × 11257¹

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 22514

List of positive integer factors of 22514 that divides 22500 without a remainder.

1, 2, 11257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22500 and 22514. The biggest common factor number is the GCF number.
So the greatest common factor 22500 and 22514 is 2.

Also check out the Least Common Multiple of 22500 and 22514