Greatest Common Factor of 200 and 208

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, 208 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 200 and 208 is 8.

GCF(200,208) = 8

GCF of 200 and 208

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

GCF of:
and

Greatest Common Factor of 200 and 208

GCF of 200 and 208 is 8

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 208


2 208
2 104
2 52
2 26
13 13
1

Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:

208 = 24×131

∴ So by taking common prime factors GCF of 200 and 208 is 8

Greatest Common Factor of 200 and 208 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 208

List of positive integer factors of 208 that divides 208 without a remainder.

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors and prime factorization of 200 and 208. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 208 is 8.

Also check out the Least Common Multiple of 200 and 208

Properties of GCF 200 and 208

(i) The GCF of 200 and 208 is associative

GCF of 200 and 208 = GCF of 208 and 200

Related Greatest Common Factor of 200

Related Greatest Common Factor of 208

Frequently Asked Questions on GCF of 200 and 208

1. What is the GCF of 200 and 208?

Answer: GCF of 200 and 208 is 8.

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 208?

Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.

4. How to Find the GCF of 200 and 208?

Answer:

Greatest Common Factor of 200 and 208 = 8

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 208

208 = 2 x 2 x 2 x 2 x 13

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 200 and 208 is 8