Mathematics, Numbers and Numerations, Algebra and Function, Operations (+, -, x, /, etc.)

Grade 3- 5

### Objective

Students learn about factors and multiples.

### Directions

Common Factors

Give students the following information about factors:

A factor is a number which divides evenly into another number. The number 6 divides evenly into 12. It is a factor of 12.

When two numbers are multiplied, they are factors of the answer.

In the equation 2 x 6 = 12, the numbers 2 and 6 are factors of 12.

The number 1 is always a factor of every number.

A common factor is a number which is a factor of two different products.

Since the number 6 is a factor of 12 and a factor of 18, it is a common factor of both numbers.

Write this sample on the board, and see if students can guess the common factors.

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The common factors are 1, 2, 3, and 6.

Common Multiples

A multiple is the number made when any two factors are multiplied together. It is the product of two factors.

In the equation 2 x 6 = 12, the number 12 is a multiple of 2 and 6.

A common multiple is a number that is a product of the same factor as another number.

The number 12 is a common multiple of both 2 and 3.

The number 6 is a common multiple of both 2 and 3.

The number 18 is a common multiple of both 2 and 3.

Some common multiples of 2 and 3 are 6, 12, and 18.

Show students the following example:

The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.

The multiples of 3 are 3, 6, 9, 12, 15, and 18.

Distribute the activity sheets to students.

### Resources

- Working with Common Factors activity sheet (one per student)
- Working with Common Multiples activity sheet (one per student)
- pencils