# Factors and Multiples

Students will find all factor pairs for a whole number. Students will determine multiples of a given number. Students will determine whether a number is prime or composite.

## Lesson Objective

The lesson is aligned to the Common Core State Standards for Mathematics – 4.OA.4 Operations and Algebraic Thinking - Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 - 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite.

## Materials Required

Calculator

## Finding all Factor Pairs

**Part A**

Two numbers are called a **factor pair** of a number when the two numbers multiplied together give the number.

Find the factor pairs of 36.

Make a table to show the factor pairs for each number.

- 12
- 48
- 51
- 88
- 96

**Part B**

A **multiple** is any number that is the product of a given number.

You can find the multiples of a number by multiplying the number by 1, 2, 3, etc.

Find the first four multiples of 6. Multiply 6 by 1, by 2, by 3, by 4. The first four multiples of 6 are 6, 12, 18, 24.

- Find the first five multiples of 2.
- Find the first four multiples of 5.
- Find the first four multiples for 7.
- Find the first three multiples for 4.
- Find the first three multiples for 3.

**Part C**

A number is a **composite** number when the number has factor pairs other than 1 and itself.

A number is a **prime** number when the number has only one factor pair, 1 and itself.

Determine whether the number is composite or prime. Explain your answer.

- 49
- 53
- 11
- 33
- 17

**Answers:**

**Part B**

- 2, 4, 6, 8, 10
- 5, 10, 15, 20
- 7, 14, 21, 28
- 4, 8, 12
- 3, 6, 9

**Part C**

- 49 is composite because there are two factor pairs 1, 49 and 7, 7
- 53 is prime because the only factor pair is 1, 53
- 11 is prime because the only factor pair is 1, 11
- 33 is composite because there are two factor pairs 1, 33 and 3, 11
- 17 is prime because the only factor pair is 1, 17

**Individual or Group Work:**

Make a table to show the factor pairs for each number. Then determine whether the number is prime or composite.

- 7
- 56
- 22
- 13
- 81

Find the first four multiples for each number.

- 1
- 8
- 9
- 10

**10. **12

**Answers:**

Make a table to show the factor pairs for each number. Then determine whether the number is prime or composite.

Find the first four multiples for each number.

- 1, 2, 3, 4
- 8, 16, 24, 32
- 9, 18, 27, 36
- 10, 20, 30, 40
- 12, 24, 36, 48