Number Systems 2

AMDG

Number Systems 2

LESSON 2

Expressing a number as a product of its prime factors.

Practice questions

Find the prime factors of the following numbers and express

them as a product of prime numbers.

a) 12

b) 32

c) 36

d) 231

e) 44

RECAP - Prime, Even & Odd Numbers

EVEN NUMBER - A number that can be exactly divided by 2.

ODD NUMBER - A number that cannot be divided exactly into pairs.

PRIME NUMBER - A number divisible only by itself and 1.

Prime Factors.

Find the prime factors of 18.

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

Of these, 2 and 3 are prime numbers, so 2 and 3 are the prime

factors of 18.

Prime factors of 18

An easy way to find prime factors is to divide by the prime

numbers in order, smallest first.

Multiple Select

1. List the prime factors of 15.

• 3

• 1

• 5

• 15

Multiple Select

2. List the prime factors of 40.

• 10

• 5

• 2

• 8

Expressing a number as a product of its prime factors.

We've already covered the first part of this process by finding the prime factors of 18 in the table.

Example 1

Find the prime factors of 24 and express it as a product of
prime numbers: 

 $24=2\ \times2\times2\times3$  OR
 $24=2^3\times3$  

Example 2

Find the prime factors of 75 and express it as a product of prime numbers:
 $75=3\times5\times5$  OR

 $75=3\times5^2$