What is the Greatest Common Factor of 22191 and 22200?

Greatest common factor (GCF) of 22191 and 22200 is 3.

GCF(22191,22200) = 3

We will now calculate the prime factors of 22191 and 22200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22191 and 22200.

How to find the GCF of 22191 and 22200?

We will first find the prime factorization of 22191 and 22200. After we will calculate the factors of 22191 and 22200 and find the biggest common factor number .

Step-1: Prime Factorization of 22191

Prime factors of 22191 are 3, 13, 569. Prime factorization of 22191 in exponential form is:

22191 = 3¹ × 13¹ × 569¹

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 22191

List of positive integer factors of 22191 that divides 22191 without a remainder.

1, 3, 13, 39, 569, 1707, 7397

Step-4: Factors of 22200

List of positive integer factors of 22200 that divides 22191 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 22191 and 22200. The biggest common factor number is the GCF number.
So the greatest common factor 22191 and 22200 is 3.

Also check out the Least Common Multiple of 22191 and 22200