Greatest Common Factor of 14 and 16

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

Greatest common factor (GCF) of 14 and 16 is 2.

GCF(14,16) = 2

GCF of 14 and 16

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

GCF of:
and

Greatest Common Factor of 14 and 16

GCF of 14 and 16 is 2

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 16


2 16
2 8
2 4
2 2
1

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 24

∴ So by taking common prime factors GCF of 14 and 16 is 2

Greatest Common Factor of 14 and 16 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 16

List of positive integer factors of 16 that divides 16 without a remainder.

1,2,4,8,16

Greatest Common Factor

We found the factors and prime factorization of 14 and 16. The biggest common factor number is the GCF number.
So the greatest common factor 14 and 16 is 2.

Also check out the Least Common Multiple of 14 and 16

Properties of GCF 14 and 16

(i) The GCF of 14 and 16 is associative

GCF of 14 and 16 = GCF of 16 and 14

Related Greatest Common Factor of 14

Related Greatest Common Factor of 16

Frequently Asked Questions on GCF of 14 and 16

1. What is the GCF of 14 and 16?

Answer: GCF of 14 and 16 is 2.

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 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

4. How to Find the GCF of 14 and 16?

Answer:

Greatest Common Factor of 14 and 16 = 2

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

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 14 and 16 is 2