# Greatest Common Factor of 6 and 14

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 6, 14 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 6 and 14 is 2.

GCF(6,14) = 2

## GCF of 6 and 14

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

GCF of:
and

### Greatest Common Factor of 6 and 14 by Prime factorization method

Prime Factorization of 6

 2 6 3 3 1

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 21×31

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

∴ So by taking common prime factors GCF of 6 and 14 is 2

### Greatest Common Factor of 6 and 14 by matching factors method

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1,2,3,6

Factors of 14

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

1,2,7,14

Greatest Common Factor

We found the factors and prime factorization of 6 and 14. The biggest common factor number is the GCF number.
So the greatest common factor 6 and 14 is 2.

Also check out the Least Common Multiple of 6 and 14

### Properties of GCF 6 and 14

(i) The GCF of 6 and 14 is associative

GCF of 6 and 14 = GCF of 14 and 6

### Frequently Asked Questions on GCF of 6 and 14

1. What is the GCF of 6 and 14?

Answer: GCF of 6 and 14 is 2.

2. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

3. 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.

4. How to Find the GCF of 6 and 14?

Greatest Common Factor of 6 and 14 = 2

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 14

14 = 2 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 6 and 14 is 2