Greatest Common Factor of 200 and 205

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, 205 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 200 and 205 is 5.

GCF(200,205) = 5

GCF of 200 and 205

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

GCF of:
and

Greatest Common Factor of 200 and 205

GCF of 200 and 205 is 5

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 205


5 205
41 41
1

Prime factors of 205 are 5,41. Prime factorization of 205 in exponential form is:

205 = 51×411

∴ So by taking common prime factors GCF of 200 and 205 is 5

Greatest Common Factor of 200 and 205 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 205

List of positive integer factors of 205 that divides 205 without a remainder.

1,5,41,205

Greatest Common Factor

We found the factors and prime factorization of 200 and 205. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 205 is 5.

Also check out the Least Common Multiple of 200 and 205

Properties of GCF 200 and 205

(i) The GCF of 200 and 205 is associative

GCF of 200 and 205 = GCF of 205 and 200

Related Greatest Common Factor of 200

Related Greatest Common Factor of 205

Frequently Asked Questions on GCF of 200 and 205

1. What is the GCF of 200 and 205?

Answer: GCF of 200 and 205 is 5.

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 205?

Answer: Factors of 205 are 1, 5, 41, 205. There are 4 integers that are factors of 205. The greatest factor of 205 is 205.

4. How to Find the GCF of 200 and 205?

Answer:

Greatest Common Factor of 200 and 205 = 5

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 205

205 = 5 x 41

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

GCF = 5

Step 4: Therefore, the greatest common factor of 200 and 205 is 5