Factors and Multiples

By Donna Ventura

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

Factors and Multiples Lesson Examples 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.

  1. 12
  2. 48
  3. 51
  4. 88
  5. 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.

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

  1. 49
  2. 53
  3. 11
  4. 33
  5. 17

Answers:

Part B

  1. 2, 4, 6, 8, 10
  2. 5, 10, 15, 20
  3. 7, 14, 21, 28
  4. 4, 8, 12
  5. 3, 6, 9

Part C

  1. 49 is composite because there are two factor pairs 1, 49 and 7, 7
  2. 53 is prime because the only factor pair is 1, 53
  3. 11 is prime because the only factor pair is 1, 11
  4. 33 is composite because there are two factor pairs 1, 33 and 3, 11
  5. 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.

  1. 7
  2. 56
  3. 22
  4. 13
  5. 81

Find the first four multiples for each number.

  1. 1
  2. 8
  3. 9
  4. 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. 1, 2, 3, 4
  2. 8, 16, 24, 32
  3. 9, 18, 27, 36
  4. 10, 20, 30, 40
  5. 12, 24, 36, 48