Greatest Common Factor of 12 and 14

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 12, 14 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 12 and 14 is 2.

GCF(12,14) = 2

GCF of 12 and 14

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

GCF of:
and

Greatest Common Factor of 12 and 14

GCF of 12 and 14 is 2

Prime Factorization of 12


2 12
2 6
3 3
1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

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 12 and 14 is 2

Greatest Common Factor of 12 and 14 by matching factors method

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

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 12 and 14. The biggest common factor number is the GCF number.
So the greatest common factor 12 and 14 is 2.

Also check out the Least Common Multiple of 12 and 14

Properties of GCF 12 and 14

(i) The GCF of 12 and 14 is associative

GCF of 12 and 14 = GCF of 14 and 12

Related Greatest Common Factor of 12

Related Greatest Common Factor of 14

Frequently Asked Questions on GCF of 12 and 14

1. What is the GCF of 12 and 14?

Answer: GCF of 12 and 14 is 2.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

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 12 and 14?

Answer:

Greatest Common Factor of 12 and 14 = 2

Step 1: Find the prime factorization of 12

12 = 2 x 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 12 and 14 is 2