Factors and Multiples

When two numbers are multiplied to get a third number, the two numbers are factors.
Consider: a x b = c ,    a and b are factors of c. c is referred to as the Multiple.
A composite number is a number with more than two factors.

Factors of Composite numbers

a) Write all the factors of 32
b) Express 32 as a product of two factors in 3 ways

a) Factors of 32 are:
1, 2, 4, 8, 16, 32

b) 24
   = 1 x 32
   = 2 x 16
   = 8 x 4

Prime Factors

A prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers.
E.g 2, 3, 5, 7, 11, 23.
a) Write 120 as a product of it’s prime factors in power form.

120
   = 2 x 60
   = 2 x 2 x 30
   = 2 x 2 x 2 x 15
   = 2 x 2 x 2 x 3 x 5
   = 2³ x 3 x 5

The above example can be presented using the factor tree method

b) Expand and find the value of 2⁴ x 7² x 11

2⁴ x 7² x 11
   = 2 x 2 x 2 x 2 x 7 x 7 x 11
   = 16 x 49 x 11
   = 8624