What is the Greatest Common Factor of 200 and 218?

Greatest common factor (GCF) of 200 and 218 is 2.

GCF(200,218) = 2

We will now calculate the prime factors of 200 and 218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 200 and 218.

How to find the GCF of 200 and 218?

We will first find the prime factorization of 200 and 218. After we will calculate the factors of 200 and 218 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 218

Prime factors of 218 are 2, 109. Prime factorization of 218 in exponential form is:

218 = 2¹ × 109¹

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 218

List of positive integer factors of 218 that divides 200 without a remainder.

1, 2, 109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 200 and 218. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 218 is 2.

Also check out the Least Common Multiple of 200 and 218