Whole Numbers, Common Multiples & Prime Factor – JSS2 Mathematics Lesson Note (First Term)

A factor of a number is a whole number that divides it exactly, and a multiple is the result of multiplying the number by a whole number. A prime number has exactly two factors, 1 and itself. Numbers can be expressed as a product of prime factors in index notation, for example 56 = 2³ × 7.

Behavioural objectives

By the end of the lesson, students should be able to:

• find all the factors of a whole number;
• write the multiples of a whole number;
• identify prime numbers and say which factors of a number are prime or even;
• express a number as a product of prime factors in index notation.

What are factors?

A factor of a number is a whole number that divides the number exactly. For example, the factors of 18 may be found as follows:

• 18 = 1 × 18
• 18 = 2 × 9
• 18 = 3 × 6

What are multiples?

A multiple of a number is obtained by multiplying it by any whole number. For example, the multiples of 4 are 4, 8, 12, 16, 20, 24 and so on.

What is a prime number?

A prime number is a number that has only two factors, which are 1 and itself. Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19 and so on.

Worked examples on factors and multiples

Example 1

(a) Find all the factors of 18.
(b) State which of these factors are even.
(c) State which of these factors are prime numbers.
(d) Write the first three multiples of 18.

Solution

• (a) The factors of 18 are 1, 2, 3, 6, 9 and 18.
• (b) The even factors are 2, 6 and 18.
• (c) The prime factors are 2 and 3.
• (d) The first three multiples of 18 are 18, 36 and 54.

Example 2

Find the factors of 56.

Solution

• 1 × 56
• 2 × 28
• 4 × 14
• 7 × 8

Therefore, the factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.

How do we write a number as a product of prime factors?

To write a number as a product of prime factors, every factor in the product must be a prime number. Repeated factors are then written in index notation.

Example 3

Express 56 and 108 as the product of prime factors in index notation.

Solution

• 56 = 2 × 2 × 2 × 7 = 2³ × 7
• 108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

Evaluation

1. Find all the factors of 24.
2. Write the first five multiples of 6.
3. List the prime numbers from 2 to 19.
4. Express 56 as a product of prime factors in index notation.

Assignment

1. Find all the factors of 36 and state which of them are prime numbers.
2. Write the first four multiples of 12.
3. Express 36 as a product of prime factors in index notation.