Greatest Common Factor of 209 and 217

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 209, 217 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 209 and 217 is 1.

GCF(209,217) = 1

GCF of 209 and 217

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

GCF of:
and

Greatest Common Factor of 209 and 217

GCF of 209 and 217 is 1

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

Prime Factorization of 217


7 217
31 31
1

Prime factors of 217 are 7,31. Prime factorization of 217 in exponential form is:

217 = 71×311

∴ So by taking common prime factors GCF of 209 and 217 is 1

Greatest Common Factor of 209 and 217 by matching factors method

Factors of 209

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

1,11,19,209

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1,7,31,217

Greatest Common Factor

We found the factors and prime factorization of 209 and 217. The biggest common factor number is the GCF number.
So the greatest common factor 209 and 217 is 1.

Also check out the Least Common Multiple of 209 and 217

Properties of GCF 209 and 217

(i) The GCF of 209 and 217 is associative

GCF of 209 and 217 = GCF of 217 and 209

Related Greatest Common Factor of 209

Related Greatest Common Factor of 217

Frequently Asked Questions on GCF of 209 and 217

1. What is the GCF of 209 and 217?

Answer: GCF of 209 and 217 is 1.

2. 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.

3. What are the Factors of 217?

Answer: Factors of 217 are 1, 7, 31, 217. There are 4 integers that are factors of 217. The greatest factor of 217 is 217.

4. How to Find the GCF of 209 and 217?

Answer:

Greatest Common Factor of 209 and 217 = 1

Step 1: Find the prime factorization of 209

209 = 11 x 19

Step 2: Find the prime factorization of 217

217 = 7 x 31

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 209 and 217 is 1