Greatest Common Factor of 209 and 214

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

Greatest common factor (GCF) of 209 and 214 is 1.

GCF(209,214) = 1

GCF of 209 and 214

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

GCF of:
and

Greatest Common Factor of 209 and 214

GCF of 209 and 214 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 214


2 214
107 107
1

Prime factors of 214 are 2,107. Prime factorization of 214 in exponential form is:

214 = 21×1071

∴ So by taking common prime factors GCF of 209 and 214 is 1

Greatest Common Factor of 209 and 214 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 214

List of positive integer factors of 214 that divides 214 without a remainder.

1,2,107,214

Greatest Common Factor

We found the factors and prime factorization of 209 and 214. The biggest common factor number is the GCF number.
So the greatest common factor 209 and 214 is 1.

Also check out the Least Common Multiple of 209 and 214

Properties of GCF 209 and 214

(i) The GCF of 209 and 214 is associative

GCF of 209 and 214 = GCF of 214 and 209

Related Greatest Common Factor of 209

Related Greatest Common Factor of 214

Frequently Asked Questions on GCF of 209 and 214

1. What is the GCF of 209 and 214?

Answer: GCF of 209 and 214 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 214?

Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.

4. How to Find the GCF of 209 and 214?

Answer:

Greatest Common Factor of 209 and 214 = 1

Step 1: Find the prime factorization of 209

209 = 11 x 19

Step 2: Find the prime factorization of 214

214 = 2 x 107

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 214 is 1