Greatest Common Factor of 12 and 15

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, 15 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 12 and 15 is 3.

GCF(12,15) = 3

GCF of 12 and 15

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

GCF of:
and

Greatest Common Factor of 12 and 15

GCF of 12 and 15 is 3

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 15


3 15
5 5
1

Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:

15 = 31×51

∴ So by taking common prime factors GCF of 12 and 15 is 3

Greatest Common Factor of 12 and 15 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 15

List of positive integer factors of 15 that divides 15 without a remainder.

1,3,5,15

Greatest Common Factor

We found the factors and prime factorization of 12 and 15. The biggest common factor number is the GCF number.
So the greatest common factor 12 and 15 is 3.

Also check out the Least Common Multiple of 12 and 15

Properties of GCF 12 and 15

(i) The GCF of 12 and 15 is associative

GCF of 12 and 15 = GCF of 15 and 12

Related Greatest Common Factor of 12

Related Greatest Common Factor of 15

Frequently Asked Questions on GCF of 12 and 15

1. What is the GCF of 12 and 15?

Answer: GCF of 12 and 15 is 3.

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 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

4. How to Find the GCF of 12 and 15?

Answer:

Greatest Common Factor of 12 and 15 = 3

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 15

15 = 3 x 5

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 12 and 15 is 3