*Contributor: Ashley Nail Murphy. Lesson ID: 13405*

What are factors and multiples? How are they similar, and how are they different? Solve an important riddle and become an expert on factors and multiples!

categories

subject

Math

learning style

Visual

personality style

Lion, Beaver

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

Ailee says 2 is a factor of 16, and 16 is a multiple of 2; however, 4 is a factor of 16 and also a multiple of 2.

Wow! That seems confusing!

- Is Ailee's statement true?

- Where do we even start to discover if Ailee is correct?

The first step to discovering if Ailee's statement is true is to look at the vocabulary words.

Yes! Math has vocabulary, and it is so important in understanding confusing topics.

First, we need to define the words *factor* and *multiple*.

- You may have heard of these words before, but do you really understand what they mean?

**Factors**

Look at these parts of a multiplication equation:

A factor is the number being multiplied by another factor to make a product.

So in this equation, 2 and 10 are the factors of 20.

Let's try a few more:

So now that you know 2 and 10 are factors of 20, try thinking of any other factors that make 20 when multiplied together.

- Can you think of any more multiplication equations that equal 20?

Yes! 4 x 5 and 1 x 20 are also factors that, when multiplied, make the product of 20.

To make a list of the factors of 20, you list them in order from least to greatest:

So, the factors of 20 are 1, 2, 4, 5, 10, 20.

Let's try a few more:

**Multiples**

Multiples are related to factors because a multiple is the product of a given number by another whole number. Multiples are also what you get when you skip count.

For example, let's find the multiples of 3.

3 becomes a factor, and then we multiply it by each whole number.

We start with the multiplication equations of 3 x 1 = 3 and continue on.

- Could we continue finding multiples of 3?

Yes!

To make a list of the multiples of 3, you list them in order from least to greatest:

The list also shows skip counting by 3.

Let's try a few more:

**Factors vs. Multiples**

Now, let's compare the two vocabulary words using 10 as an example:

Factors |
Multiples |

- numbers multiplied together to make a product for a given number:
2 x 5 = 10 |
- product of a given number multiplied by a whole number:
10 x 2 = 20 |

- list all multiplication math facts for given numbers:
2 x 5 = 10 1 x 10 = 10 |
- make a list by skip counting:
10 20 30 etc. |

- numbers are less than or equal to given number:
1 < 10 2 < 10 5 < 10 10 = 10 |
- numbers in list are greater than or equal to given number:
10 = 10 20 > 10 30 > 10 etc. |

- a specific set of numbers:
1 2 5 10 |
- list could go on forever:
10 20 30 40 50 etc. |

- Ready to practice and discover if Ailee's statement is true?

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