What is the Greatest Common Factor of 200 and 220?

Greatest common factor (GCF) of 200 and 220 is 20.

GCF(200,220) = 20

We will now calculate the prime factors of 200 and 220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 200 and 220.

How to find the GCF of 200 and 220?

We will first find the prime factorization of 200 and 220. After we will calculate the factors of 200 and 220 and find the biggest common factor number .

Step-1: Prime Factorization of 200

Prime factors of 200 are 2, 5. Prime factorization of 200 in exponential form is:

200 = 2³ × 5²

Step-2: Prime Factorization of 220

Prime factors of 220 are 2, 5, 11. Prime factorization of 220 in exponential form is:

220 = 2² × 5¹ × 11¹

Step-3: Factors of 200

List of positive integer factors of 200 that divides 200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100

Step-4: Factors of 220

List of positive integer factors of 220 that divides 200 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 200 and 220. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 220 is 20.

Also check out the Least Common Multiple of 200 and 220