Understanding The Least Common Factor Of 9 And 6

LCM of 6, 7 and 9 How to Find LCM of 6, 7, 9? from www.cuemath.com

Introduction

As a professional teacher, one of the basic concepts that we must teach students is the understanding of factors. Factors are numbers that can be divided into a given number without a remainder. For instance, the factors of 9 are 1, 3, and 9 because they can be divided into 9 without a remainder. On the other hand, the factors of 6 are 1, 2, 3, and 6.

What is the Least Common Factor?

The least common factor is the smallest factor that two or more numbers have in common. In this case, we are looking for the smallest factor that both 9 and 6 have in common. To find the least common factor, we need to list down all the factors of both numbers and find their common factors.

Listing the Factors of 9 and 6

To find the factors of 9, we can start by dividing it by 1, which gives us 9. When we divide 9 by 2, we get a remainder of 1. Similarly, when we divide it by 3, we get a remainder of 0. Therefore, the factors of 9 are 1, 3, and 9. To find the factors of 6, we can start by dividing it by 1, which gives us 6. When we divide 6 by 2, we get 3, which is a whole number. Similarly, when we divide it by 3, we get a remainder of 0. Therefore, the factors of 6 are 1, 2, 3, and 6.

Finding the Common Factors

Now that we have the factors of both 9 and 6, we can find their common factors. From the factors of 9, we can see that 3 is a common factor with 6, as it is also a factor of 6. Therefore, the least common factor of 9 and 6 is 3.

Why is the Least Common Factor Important?

The least common factor is important in mathematics because it helps us find the greatest common factor, which is the largest factor that two or more numbers have in common. The greatest common factor is useful in simplifying fractions, finding equivalent fractions, and solving equations.

Examples of Finding the Least Common Factor

Let us consider another example to help us understand the concept of the least common factor. Suppose we want to find the least common factor of 12 and 20. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 20 are 1, 2, 4, 5, 10, and 20. The common factors of 12 and 20 are 1, 2, and 4. Therefore, the least common factor of 12 and 20 is 2.

Conclusion

In conclusion, the least common factor is the smallest factor that two or more numbers have in common. To find the least common factor, we need to list down all the factors of the given numbers and find their common factors. The least common factor is important in mathematics because it helps us find the greatest common factor, which is useful in simplifying fractions, finding equivalent fractions, and solving equations.