What is the Greatest Common Factor of 2200 and 2218?

Greatest common factor (GCF) of 2200 and 2218 is 2.

GCF(2200,2218) = 2

We will now calculate the prime factors of 2200 and 2218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2200 and 2218.

How to find the GCF of 2200 and 2218?

We will first find the prime factorization of 2200 and 2218. After we will calculate the factors of 2200 and 2218 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 2218

Prime factors of 2218 are 2, 1109. Prime factorization of 2218 in exponential form is:

2218 = 2¹ × 1109¹

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 2218

List of positive integer factors of 2218 that divides 2200 without a remainder.

1, 2, 1109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2200 and 2218. The biggest common factor number is the GCF number.
So the greatest common factor 2200 and 2218 is 2.

Also check out the Least Common Multiple of 2200 and 2218