What is the Greatest Common Factor of 2200 and 2214?

Greatest common factor (GCF) of 2200 and 2214 is 2.

GCF(2200,2214) = 2

We will now calculate the prime factors of 2200 and 2214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2200 and 2214.

How to find the GCF of 2200 and 2214?

We will first find the prime factorization of 2200 and 2214. After we will calculate the factors of 2200 and 2214 and find the biggest common factor number .

Step-1: Prime Factorization of 2200

Prime factors of 2200 are 2, 5, 11. Prime factorization of 2200 in exponential form is:

2200 = 2³ × 5² × 11¹

Step-2: Prime Factorization of 2214

Prime factors of 2214 are 2, 3, 41. Prime factorization of 2214 in exponential form is:

2214 = 2¹ × 3³ × 41¹

Step-3: Factors of 2200

List of positive integer factors of 2200 that divides 2200 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100

Step-4: Factors of 2214

List of positive integer factors of 2214 that divides 2200 without a remainder.

1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2200 and 2214. The biggest common factor number is the GCF number.
So the greatest common factor 2200 and 2214 is 2.

Also check out the Least Common Multiple of 2200 and 2214