Learning Objectives:

__Math Tutoring on Factors, Prime Factors, and Least Common Multiples__

*Factors of Natural Numbers (1, 2, 3, 4, 5 …):*

**Factors** are the numbers that divide evenly into a number. This means a **Factor** divides into another number and there is no remainder.

If we let **“N”** be a **Natural Number** and, then **x** and **y**** **are **Factors** of **N**.

A **Prime Number** is a natural number greater than 1 that only has two **factors**: one and itself. Example: 2, 3, 5, 7, 11, 13, 17, 19, 23 … So the process of factorization of an integer to a series of **Prime Numbers** is called **Prime Factorization** and the factors are called **Prime Factors**.

A **Composite Number** is a natural number that has more than two factors. The number ‘1’ is either **Prime** or **Composite**.

The **(LCM) Least Common Multiple** or **Lowest Common Multiple** of two rational number **‘a’** and **‘b’** is the smallest positive rational number that is an integer multiple of both **‘a’** and **‘b’**. Since it is multiple, it can be divided by **‘a’** and **‘b’** without a remainder.

The method of writing out multiplies is only practical for determining the **LCM** of small numbers. As a result, we have a different way to build the **LCM** of two numbers by analyzing **Prime Factors**.

The **LCM** must contain all of the different factors in the terms and each factor must be repeated the maximum number of times it occurs in any one of the terms.

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**Hook Questions:**

*1. **What is the Factorization Process of a number?*

*2. **What are called Prime Factors? How is it obtained?*

*3. **What is the Least Common Multiple?*

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