What is the Greatest Common Factor of 200 and 210?

Greatest common factor (GCF) of 200 and 210 is 10.

GCF(200,210) = 10

We will now calculate the prime factors of 200 and 210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 200 and 210.

How to find the GCF of 200 and 210?

We will first find the prime factorization of 200 and 210. After we will calculate the factors of 200 and 210 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 210

Prime factors of 210 are 2, 3, 5, 7. Prime factorization of 210 in exponential form is:

210 = 2¹ × 3¹ × 5¹ × 7¹

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 210

List of positive integer factors of 210 that divides 200 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 200 and 210. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 210 is 10.

Also check out the Least Common Multiple of 200 and 210