Factors and Multiples

Factor × Factor = Multiple


Basics

Factor × Factor = Multiple
A factor is what is multiplied.
A multiple is the product of factors.

Multiple ÷ Factor = Factor
Factoring uses division to determine the factors of multiples.

In order to work with factors and multiples, it is helpful to know your multiplication and division tables.

The numbers 2 and 3 are often useful for division in factoring.

It is possible that questions involving simplifying square roots will require factoring in the calculator-prohibited section of the test.


Formulas (NOT provided by Mathematics Formula Sheet)

Factor × Factor = Multiple
Multiple ÷ Factor = Factor


Question

What are the factors of 18?

Answer
Factors of 18 are: 1 and 18; 2 and 9; 3 and 6.
18 is a multiple of: 1 and 18; 2 and 9; 3 and 6.

Answer Process
Factoring:
18               ÷           1               =         18
Multiple                 Factor                 Factor

18               ÷           2              =         9
Multiple                 Factor                 Factor

18               ÷           3               =         6
Multiple                 Factor                 Factor

Factors:
1          ×          18               =         18
Factor            Factor                   Multiple

2          ×          9               =         18
Factor            Factor                  Multiple

3          ×          6               =         18
Factor            Factor                  Multiple


Question

What are the factors of 24?

Answer
Factors of 24 are: 1 and 24; 2 and 12; 3 and 8; 4 and 6.
24 is a multiple of: 1 and 24; 2 and 12; 3 and 8; 4 and 6.

Answer Process
Factoring:
24               ÷           1               =         24
Multiple                 Factor                 Factor

24               ÷           2              =         12
Multiple                 Factor                 Factor

24               ÷           3               =         8
Multiple                 Factor                 Factor

24               ÷           4               =         6
Multiple                 Factor                 Factor

Factors:
1          ×          24               =         24
Factor            Factor                   Multiple

2          ×          12               =         24
Factor            Factor                   Multiple

3          ×          8               =         24
Factor            Factor                  Multiple

4          ×          6               =         24
Factor            Factor                  Multiple


Practice – Questions

1.  What are the factors of 12?  Show your work.

2.  What are the factors of 16?  Show your work.

3.  What are the factors of 32?

4.  What are the factors of 48?

5.  What are the factors of 25?


Practice – Answers

1.
Factors of 12 are: 1 and 12; 2 and 6; 3 and 4.
12 is a multiple of: 1 and 12; 2 and 6; 3 and 4.

Factoring:
12               ÷           1               =         12
Multiple                 Factor                Factor

12               ÷           2              =         6
Multiple                 Factor                Factor

12               ÷           3               =         4
Multiple                 Factor                 Factor

Factors:
1          ×          12               =         12
Factor            Factor                   Multiple

2          ×          6               =         12
Factor            Factor                  Multiple

3          ×          4               =         12
Factor            Factor                  Multiple

2.
Factors of 16 are: 1 and 16; 2 and 8; 4 and 4.
16 is a multiple of: 1 and 16; 2 and 8; 4 and 4.

Factoring:
16               ÷           1               =         16
Multiple                 Factor                Factor

16               ÷           2              =         8
Multiple                 Factor                Factor

16               ÷           4               =         4
Multiple                 Factor                 Factor

Factors:
1          ×          16               =         16
Factor            Factor                   Multiple

2          ×          8               =         16
Factor            Factor                  Multiple

4          ×          4               =         16
Factor            Factor                  Multiple

3.
Factors of 32 are: 1 and 32; 2 and 16; 4 and 8.
32 is a multiple of: 1 and 32; 2 and 16; 4 and 8.

4.
Factors of 48 are: 1 and 48; 2 and 24; 3 and 16; 4 and 12; 6 and 8.
48 is a multiple of: 1 and 48; 2 and 24; 3 and 16. 4 and 12; 6 and 8.

5.
Factors of 25 are: 1 and 25; 5 and 5.
25 is a multiple of: 1 and 25; 5 and 5.

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