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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Bethany Calderwood*

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

A mathematician needs to know how to work with numbers. In this lesson, you'll learn two ways to work with numbers: using factors and multiples. You'll also learn the definitions of factors and multiples and how to find the factors and multiples of a number.

Sylvia is in charge of a company. She assigns jobs to workers based upon their skills. For example, Sylvia asks Martin, a writer, to write an article, and Lucille, an artist, to draw a poster. Knowing the skills of her employees helps Sylvia run her company effectively.

A mathematician is like the owner of a company. The mathematician has many numbers to work with and needs to know what the numbers can do. Two important properties of numbers that a mathematician needs to know are factors and multiples.

Let's start with multiples. When you stack identical blocks one on top of one another, the result is a large tower made up of those blocks. When you add identical numbers, the sum is a larger number made up of those numbers. Those larger numbers are called **multiples**.

The multiples of a number are found by multiplying the number by any whole number. Look at the picture of the block towers. Each tower shows 1 multiple of the number 3. The first tower is 1 block of 3. The second tower is 2 blocks of 3, which equals 6. The third tower is 3 blocks of 3, which equals 9. The fourth tower is 4 blocks of 3, which equals 12. You could make infinite towers, and a number can have infinite multiples.

A few ways to find multiples are:

- Adding a number to itself repeatedly, as in 4 + 4 = 8, 8 + 4 = 12, 12 + 4 = 16, etc.
- Skip counting, as in 5, 10, 15, 20, 25, etc.
- Multiplication, as in 2 * 1 = 2, 2 * 2 = 4, 2 * 3 = 6, 2 * 4 = 8, etc.

The **factors** of a number are any whole numbers that can be multiplied by another whole number to get that number. Look at this factor tree for the number 12.

To find the factors of 12:

- We begin with 1. We know that 1 times 12 equals 12. We place the 1 on the far left and the 12 on the far right of the factor tree.

- Next we try 2. We know that 2 times 6 equals 12, so we place 2 on the left side and 6 on the right side of the factor tree.

- We try 3. We know that 3 times 4 equals 12, so we place 3 on the left side and 4 on the right side of the factor tree.

- The next number is 4, which we used already.

This factor tree is done. The factors of 12 are: 1, 2, 3, 4, 6, and 12.

Let's try another example:

To find the factors of 15:

- We begin with 1 times 15.

- We know that 2 will not divide evenly into 15, so we skip it.

- We try 3. We know that 3 times 5 equals 15, so we place 3 on the left and 5 on the right side of the factor tree.

- We know that 4 will not divide evenly into 15.

- The next number is 5, which is already on the factor tree, so we're finished.

The factors of 15 are: 1, 3, 5, and 15.

To recap, the **multiples** of a number are the results of multiplying the number by any whole number. The **factors** of a number are the numbers that divide evenly into the number. Knowledge of a number's factors and multiplies can help the mathematician to use the number in a variety of operations and equations.

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Math for Kids23 chapters | 325 lessons

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