# Greatest Common Factor of 14 and 17

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 14, 17 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 14 and 17 is 1.

GCF(14,17) = 1

## GCF of 14 and 17

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

GCF of:
and ### GCF of 14 and 17 is 1

Prime Factorization of 14

 2 14 7 7 1

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 21×71

Prime Factorization of 17

 17 17 1

Prime factors of 17 are 17. Prime factorization of 17 in exponential form is:

17 = 171

∴ So by taking common prime factors GCF of 14 and 17 is 1

### Greatest Common Factor of 14 and 17 by matching factors method

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1,17

Greatest Common Factor

We found the factors and prime factorization of 14 and 17. The biggest common factor number is the GCF number.
So the greatest common factor 14 and 17 is 1.

Also check out the Least Common Multiple of 14 and 17

### Properties of GCF 14 and 17

(i) The GCF of 14 and 17 is associative

GCF of 14 and 17 = GCF of 17 and 14

### Frequently Asked Questions on GCF of 14 and 17

1. What is the GCF of 14 and 17?

Answer: GCF of 14 and 17 is 1.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

3. What are the Factors of 17?

Answer: Factors of 17 are 1, 17. There are 2 integers that are factors of 17. The greatest factor of 17 is 17.

4. How to Find the GCF of 14 and 17?

Greatest Common Factor of 14 and 17 = 1

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 17

17 = 17

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 14 and 17 is 1