What is the Greatest Common Factor of 22200 and 22214?

Greatest common factor (GCF) of 22200 and 22214 is 2.

GCF(22200,22214) = 2

We will now calculate the prime factors of 22200 and 22214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22200 and 22214.

How to find the GCF of 22200 and 22214?

We will first find the prime factorization of 22200 and 22214. After we will calculate the factors of 22200 and 22214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 22214

Prime factors of 22214 are 2, 29, 383. Prime factorization of 22214 in exponential form is:

22214 = 2¹ × 29¹ × 383¹

Step-3: Factors of 22200

List of positive integer factors of 22200 that divides 22200 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

Step-4: Factors of 22214

List of positive integer factors of 22214 that divides 22200 without a remainder.

1, 2, 29, 58, 383, 766, 11107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22200 and 22214. The biggest common factor number is the GCF number.
So the greatest common factor 22200 and 22214 is 2.

Also check out the Least Common Multiple of 22200 and 22214