Warm Up

 

A. Factors and Multiples

In multiplication, factors are multiplied to produce a product. There can be more than one set of factors that produce the same product.

Factors
two or more numbers that are multiplied resulting in a product

Example 1

List all possible whole number factors of 36.

Factors Product
1 × 36
36
2 × 18
36
3 × 12
36
4 × 9
36
6 × 6
36

All possible whole number factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Whole number multiples result from the multiplication of an original number by an Integer.

Multiples
the result of an original number multiplied by an Integer

Integers
the set of positive and negative Whole Numbers including 0; the numbers... -3, -2, -1, 0, 1, 2, 3... are Integers

You will review the Number System more thoroughly in Lesson 4.3.

Example 2

List all whole number multiples of 9 between 1 to 100. Show how to generate the multiples by listing the factors used.

Multiples of 9 Factors
9
9 × 1
18
9 × 2
27
9 × 3
36
9 × 4
45
9 × 5
54
9 × 6
63
9 × 7
72
9 × 8
81
9 × 9
90
9 × 10
99
9 × 11