Greatest Common Factor of 12 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 12, 16 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 12 and 16 is 4.

GCF(12,16) = 4

GCF of 12 and 16

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

GCF of:
and

Greatest Common Factor of 12 and 16

GCF of 12 and 16 is 4

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 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 12 and 16 is 4

Greatest Common Factor of 12 and 16 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 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 12 and 16. The biggest common factor number is the GCF number.
So the greatest common factor 12 and 16 is 4.

Also check out the Least Common Multiple of 12 and 16

Properties of GCF 12 and 16

(i) The GCF of 12 and 16 is associative

GCF of 12 and 16 = GCF of 16 and 12

Related Greatest Common Factor of 12

Related Greatest Common Factor of 16

Frequently Asked Questions on GCF of 12 and 16

1. What is the GCF of 12 and 16?

Answer: GCF of 12 and 16 is 4.

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 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 12 and 16?

Answer:

Greatest Common Factor of 12 and 16 = 4

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

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 x 2 = 4

Step 4: Therefore, the greatest common factor of 12 and 16 is 4