What are Factors & Multiples?

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  • 0:03 Making Numbers Work for You
  • 0:36 Multiples
  • 1:48 Factors
  • 3:05 Lesson Summary
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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.

Making Numbers Work for You

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.

Multiples of 3.

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.

Factors of 12.

To find the factors of 12:

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