Greatest Common Factor of 12 and 18

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 12, 18 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 12 and 18 is 6.

GCF(12,18) = 6

GCF of 12 and 18

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

GCF of:
and

Greatest Common Factor of 12 and 18 by Prime factorization method

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 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

∴ So by taking common prime factors GCF of 12 and 18 is 6

Greatest Common Factor of 12 and 18 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 18

List of positive integer factors of 18 that divides 18 without a remainder.

1,2,3,6,9,18

Greatest Common Factor

We found the factors and prime factorization of 12 and 18. The biggest common factor number is the GCF number.
So the greatest common factor 12 and 18 is 6.

Also check out the Least Common Multiple of 12 and 18

Properties of GCF 12 and 18

(i) The GCF of 12 and 18 is associative

GCF of 12 and 18 = GCF of 18 and 12

Frequently Asked Questions on GCF of 12 and 18

1. What is the GCF of 12 and 18?

Answer: GCF of 12 and 18 is 6.

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 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

4. How to Find the GCF of 12 and 18?

Answer:

Greatest Common Factor of 12 and 18 = 6

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 18

18 = 2 x 3 x 3

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 12 and 18 is 6

Greatest Common Factor of 12 and 18