Greatest Common Factor of 208 and 209

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, 209 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 208 and 209 is 1.

GCF(208,209) = 1

GCF of 208 and 209

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

GCF of:
and

Greatest Common Factor of 208 and 209

GCF of 208 and 209 is 1

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 209


11 209
19 19
1

Prime factors of 209 are 11,19. Prime factorization of 209 in exponential form is:

209 = 111×191

∴ So by taking common prime factors GCF of 208 and 209 is 1

Greatest Common Factor of 208 and 209 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 209

List of positive integer factors of 209 that divides 209 without a remainder.

1,11,19,209

Greatest Common Factor

We found the factors and prime factorization of 208 and 209. The biggest common factor number is the GCF number.
So the greatest common factor 208 and 209 is 1.

Also check out the Least Common Multiple of 208 and 209

Properties of GCF 208 and 209

(i) The GCF of 208 and 209 is associative

GCF of 208 and 209 = GCF of 209 and 208

Related Greatest Common Factor of 208

Related Greatest Common Factor of 209

Frequently Asked Questions on GCF of 208 and 209

1. What is the GCF of 208 and 209?

Answer: GCF of 208 and 209 is 1.

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 209?

Answer: Factors of 209 are 1, 11, 19, 209. There are 4 integers that are factors of 209. The greatest factor of 209 is 209.

4. How to Find the GCF of 208 and 209?

Answer:

Greatest Common Factor of 208 and 209 = 1

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 209

209 = 11 x 19

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 208 and 209 is 1