Greatest Common Factor of 200 and 210

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 200, 210 i.e. 10 largest integer by which both the numbers can be divided.

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

GCF(200,210) = 10

GCF of 200 and 210

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 200 and 210

GCF of 200 and 210 is 10

Prime Factorization of 200


2 200
2 100
2 50
5 25
5 5
1

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

200 = 23×52

Prime Factorization of 210


2 210
3 105
5 35
7 7
1

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

210 = 21×31×51×71

∴ So by taking common prime factors GCF of 200 and 210 is 10

Greatest Common Factor of 200 and 210 by matching factors method

Factors of 200

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

1,2,4,5,8,10,20,25,40,50,100,200

Factors of 210

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

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

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

Properties of GCF 200 and 210

(i) The GCF of 200 and 210 is associative

GCF of 200 and 210 = GCF of 210 and 200

Related Greatest Common Factor of 200

Related Greatest Common Factor of 210

Frequently Asked Questions on GCF of 200 and 210

1. What is the GCF of 200 and 210?

Answer: GCF of 200 and 210 is 10.

2. What are the Factors of 200?

Answer: Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. There are 12 integers that are factors of 200. The greatest factor of 200 is 200.

3. What are the Factors of 210?

Answer: Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. There are 16 integers that are factors of 210. The greatest factor of 210 is 210.

4. How to Find the GCF of 200 and 210?

Answer:

Greatest Common Factor of 200 and 210 = 10

Step 1: Find the prime factorization of 200

200 = 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 5 = 10

Step 4: Therefore, the greatest common factor of 200 and 210 is 10