Finding the greatest common factor of two numbers is a fundamental concept in elementary mathematics. In this blog post, we’ll explore how to find the greatest common factor of 18 and 12.

Firstly, let’s define what a greatest common factor is. It’s the largest number that both numbers can be divided by without a remainder. So, what are the factors of 18 and 12?

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 12: 1, 2, 3, 4, 6, 12

We can see that the factors of 18 and 12 both include 1, 2, 3, and 6. However, the highest number that both share as a factor is 6. Therefore, the greatest common factor of 18 and 12 is 6.

Another method to find the greatest common factor is prime factorization. To do this, we need to break down both numbers into their prime factors.

18 = 2 x 3 x 3

12 = 2 x 2 x 3

We can see that both numbers share the factors 2 and 3. The highest power shared by both is 2 x 3, which equals 6. Therefore, the greatest common factor of 18 and 12 is once again 6.

In conclusion, finding the greatest common factor of two numbers involves identifying the factors of each number and finding the highest number that they share in common. Alternatively, prime factorization can also be used to identify the greatest common factor. In the case of 18 and 12, the greatest common factor is 6.