What is the Greatest Common Factor of 22185 and 22200?

Greatest common factor (GCF) of 22185 and 22200 is 15.

GCF(22185,22200) = 15

We will now calculate the prime factors of 22185 and 22200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22185 and 22200.

How to find the GCF of 22185 and 22200?

We will first find the prime factorization of 22185 and 22200. After we will calculate the factors of 22185 and 22200 and find the biggest common factor number .

Step-1: Prime Factorization of 22185

Prime factors of 22185 are 3, 5, 17, 29. Prime factorization of 22185 in exponential form is:

22185 = 3² × 5¹ × 17¹ × 29¹

Step-2: Prime Factorization of 22200

Prime factors of 22200 are 2, 3, 5, 37. Prime factorization of 22200 in exponential form is:

22200 = 2³ × 3¹ × 5² × 37¹

Step-3: Factors of 22185

List of positive integer factors of 22185 that divides 22185 without a remainder.

1, 3, 5, 9, 15, 17, 29, 45, 51, 85, 87, 145, 153, 255, 261, 435, 493, 765, 1305, 1479, 2465, 4437, 7395

Step-4: Factors of 22200

List of positive integer factors of 22200 that divides 22185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 37, 40, 50, 60, 74, 75, 100, 111, 120, 148, 150, 185, 200, 222, 296, 300, 370, 444, 555, 600, 740, 888, 925, 1110, 1480, 1850, 2220, 2775, 3700, 4440, 5550, 7400, 11100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22185 and 22200. The biggest common factor number is the GCF number.
So the greatest common factor 22185 and 22200 is 15.

Also check out the Least Common Multiple of 22185 and 22200