What Is The Gcf Of 9 And 12?

GCF of 9 and 12 How to Find GCF of 9, 12? from www.cuemath.com

Introduction

The greatest common factor (GCF) is the largest number that divides two or more numbers without leaving a remainder. It is an important concept in mathematics, as it is used in various calculations and problem-solving.

What are 9 and 12?

Before we can find the GCF of 9 and 12, we need to know what these numbers are. 9 and 12 are both integers, which means they are whole numbers that can be positive, negative, or zero. In this case, both 9 and 12 are positive integers.

How to Find the GCF of 9 and 12?

There are different methods to find the GCF of two numbers, but one of the most common ones is the prime factorization method. In this method, we find the prime factors of each number and then find the common factors.

Prime Factorization of 9

To find the prime factors of 9, we can start by dividing it by the smallest prime number, which is 2. However, 2 is not a factor of 9, so we move on to the next prime number, which is 3. 3 is a factor of 9, so we divide 9 by 3 to get 3. Since 3 is also a prime number, we stop here. Therefore, the prime factorization of 9 is 3 x 3.

Prime Factorization of 12

To find the prime factors of 12, we can start by dividing it by 2, which is a prime number. 2 is a factor of 12, so we divide 12 by 2 to get 6. 2 is still a factor of 6, so we divide 6 by 2 to get 3. Since 3 is a prime number, we stop here. Therefore, the prime factorization of 12 is 2 x 2 x 3.

Finding the Common Factors

Now that we have the prime factorization of both 9 and 12, we can find the common factors. The common factors are the prime factors that are shared by both numbers. In this case, the only common prime factor is 3. Therefore, the GCF of 9 and 12 is 3.

Conclusion

In conclusion, the GCF of 9 and 12 is 3. By using the prime factorization method, we can easily find the GCF of two or more numbers. It is important to understand the concept of GCF, as it is used in various mathematical calculations and problem-solving.