Greatest Common Factor of 204 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 204, 210 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 204 and 210 is 6.

GCF(204,210) = 6

GCF of 204 and 210

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

GCF of:
and

Greatest Common Factor of 204 and 210

GCF of 204 and 210 is 6

Prime Factorization of 204


2 204
2 102
3 51
17 17
1

Prime factors of 204 are 2,3,17. Prime factorization of 204 in exponential form is:

204 = 22×31×171

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 204 and 210 is 6

Greatest Common Factor of 204 and 210 by matching factors method

Factors of 204

List of positive integer factors of 204 that divides 204 without a remainder.

1,2,3,4,6,12,17,34,51,68,102,204

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 204 and 210. The biggest common factor number is the GCF number.
So the greatest common factor 204 and 210 is 6.

Also check out the Least Common Multiple of 204 and 210

Properties of GCF 204 and 210

(i) The GCF of 204 and 210 is associative

GCF of 204 and 210 = GCF of 210 and 204

Related Greatest Common Factor of 204

Related Greatest Common Factor of 210

Frequently Asked Questions on GCF of 204 and 210

1. What is the GCF of 204 and 210?

Answer: GCF of 204 and 210 is 6.

2. What are the Factors of 204?

Answer: Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204. There are 12 integers that are factors of 204. The greatest factor of 204 is 204.

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 204 and 210?

Answer:

Greatest Common Factor of 204 and 210 = 6

Step 1: Find the prime factorization of 204

204 = 2 x 2 x 3 x 17

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 3 = 6

Step 4: Therefore, the greatest common factor of 204 and 210 is 6