Greatest Common Factor of 208 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 208, 210 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 208 and 210 is 2.

GCF(208,210) = 2

GCF of 208 and 210

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

GCF of:
and

Greatest Common Factor of 208 and 210

GCF of 208 and 210 is 2

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

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 208 and 210 is 2

Greatest Common Factor of 208 and 210 by matching factors method

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

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 208 and 210. The biggest common factor number is the GCF number.
So the greatest common factor 208 and 210 is 2.

Also check out the Least Common Multiple of 208 and 210

Properties of GCF 208 and 210

(i) The GCF of 208 and 210 is associative

GCF of 208 and 210 = GCF of 210 and 208

Related Greatest Common Factor of 208

Related Greatest Common Factor of 210

Frequently Asked Questions on GCF of 208 and 210

1. What is the GCF of 208 and 210?

Answer: GCF of 208 and 210 is 2.

2. 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.

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 208 and 210?

Answer:

Greatest Common Factor of 208 and 210 = 2

Step 1: Find the prime factorization of 208

208 = 2 x 2 x 2 x 2 x 13

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

Step 4: Therefore, the greatest common factor of 208 and 210 is 2