What is the Greatest Common Factor of 200 and 214?

Greatest common factor (GCF) of 200 and 214 is 2.

GCF(200,214) = 2

We will now calculate the prime factors of 200 and 214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 200 and 214.

How to find the GCF of 200 and 214?

We will first find the prime factorization of 200 and 214. After we will calculate the factors of 200 and 214 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 214

Prime factors of 214 are 2, 107. Prime factorization of 214 in exponential form is:

214 = 2¹ × 107¹

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 214

List of positive integer factors of 214 that divides 200 without a remainder.

1, 2, 107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 200 and 214. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 214 is 2.

Also check out the Least Common Multiple of 200 and 214