Greatest Common Factor of 200 and 204

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, 204 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 200 and 204 is 4.

GCF(200,204) = 4

GCF of 200 and 204

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

GCF of:
and

Greatest Common Factor of 200 and 204

GCF of 200 and 204 is 4

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 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

∴ So by taking common prime factors GCF of 200 and 204 is 4

Greatest Common Factor of 200 and 204 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 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

Greatest Common Factor

We found the factors and prime factorization of 200 and 204. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 204 is 4.

Also check out the Least Common Multiple of 200 and 204

Properties of GCF 200 and 204

(i) The GCF of 200 and 204 is associative

GCF of 200 and 204 = GCF of 204 and 200

Related Greatest Common Factor of 200

Related Greatest Common Factor of 204

Frequently Asked Questions on GCF of 200 and 204

1. What is the GCF of 200 and 204?

Answer: GCF of 200 and 204 is 4.

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 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.

4. How to Find the GCF of 200 and 204?

Answer:

Greatest Common Factor of 200 and 204 = 4

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 204

204 = 2 x 2 x 3 x 17

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 200 and 204 is 4