Understanding The Least Common Factor Of 9 And 15

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Introduction

As a professional teacher, it is important to provide clear explanations and solutions to mathematical problems. One such problem is determining the least common factor of 9 and 15. This article aims to provide a relaxed explanation of this problem and its solution.

What is a Factor?

Before we can understand the least common factor of 9 and 15, we must first understand what a factor is. In mathematics, a factor is a number that divides evenly into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

What is the Common Factor of 9 and 15?

To determine the common factor of 9 and 15, we need to find all the factors of each number. The factors of 9 are 1, 3, and 9, while the factors of 15 are 1, 3, 5, and 15. Therefore, the common factors of 9 and 15 are 1 and 3.

What is the Least Common Factor?

The least common factor, also known as the least common multiple, is the smallest factor that is common to two or more numbers. To find the least common factor of 9 and 15, we need to find the smallest number that both 9 and 15 can be divided by evenly.

Using Prime Factorization

One method to find the least common factor is to use prime factorization. This involves breaking down each number into its prime factors and then multiplying the common factors. The prime factors of 9 are 3 x 3, and the prime factors of 15 are 3 x 5. The common prime factor is 3, so we multiply 3 x 3 x 5 to get 45. Therefore, the least common factor of 9 and 15 is 45.

Using the Division Method

Another method to find the least common factor is to use the division method. This involves dividing each number by its common factors until no more common factors can be divided out. The common factors of 9 and 15 are 1 and 3. We divide 9 by 3 to get 3, and we divide 15 by 3 to get 5. Since there are no more common factors, we multiply 3 x 5 to get 15. Therefore, the least common factor of 9 and 15 is 15.

Conclusion

In conclusion, the least common factor of 9 and 15 can be found using either the prime factorization method or the division method. Both methods will give the same result, which is 15. As a teacher, it is important to provide students with multiple strategies to solve mathematical problems and allow them to choose the one that works best for them.