Class 4 — Mathematics

Factors and Multiples

Class 4

✓By the end of this lesson students will be able to define and identify factors of a given number.
✓By the end of this lesson students will be able to define and identify multiples of a given number.
✓By the end of this lesson students will be able to list factors and multiples of numbers up to 100.
✓By the end of this lesson students will be able to find common factors of two given numbers.
✓By the end of this lesson students will be able to find common multiples of two given numbers.

Key concepts

Factors

A factor of a number is a number that divides it exactly, without leaving any remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 completely.

Multiples

A multiple of a number is the product of that number and any other whole number (1, 2, 3, ...). It is like counting by that number. For example, the multiples of 5 are 5, 10, 15, 20, 25, and so on, which are obtained by multiplying 5 by 1, 2, 3, 4, 5, etc.

Common Factors

When we list the factors of two or more numbers, the factors that are present in all the lists are called common factors. For example, the factors of 6 are 1, 2, 3, 6 and the factors of 9 are 1, 3, 9. The common factors of 6 and 9 are 1 and 3.

Common Multiples

When we list the multiples of two or more numbers, the multiples that are present in all the lists are called common multiples. For example, the multiples of 2 are 2, 4, 6, 8, 10, 12, ... and the multiples of 3 are 3, 6, 9, 12, 15, ... The common multiples of 2 and 3 are 6, 12, and so on.

Key facts to remember

11 is a factor of every number.
2Every number is a factor of itself.
3Factors of a number are always less than or equal to the number.
4Every number has a finite (limited) number of factors.
5The smallest multiple of a number is the number itself.
6Multiples of a number are always greater than or equal to the number.
7Every number has an infinite (unlimited) number of multiples.
8Every number is a multiple of 1.

Worked examples

Example 1

Find all the factors of 24.

ITo find factors, we check which numbers divide 24 exactly.

II1 × 24 = 24. So, 1 and 24 are factors.

III2 × 12 = 24. So, 2 and 12 are factors.

IV3 × 8 = 24. So, 3 and 8 are factors.

V4 × 6 = 24. So, 4 and 6 are factors.

VIThe next number to check is 5 (does not divide 24 exactly).

VIIThe next number is 6, which we have already found. So, we stop here.

Answer

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

Always list factors in ascending order.

Example 2

Write the first 6 multiples of 7.

ITo find the first 6 multiples, we multiply 7 by 1, 2, 3, 4, 5, and 6.

IIFirst multiple: 7 × 1 = 7

IIISecond multiple: 7 × 2 = 14

IVThird multiple: 7 × 3 = 21

VFourth multiple: 7 × 4 = 28

VIFifth multiple: 7 × 5 = 35

VIISixth multiple: 7 × 6 = 42

Answer

The first 6 multiples of 7 are 7, 14, 21, 28, 35, 42.

Multiples of a number are infinite.

Example 3

Find the common factors of 10 and 15.

IStep 1: List all the factors of 10.

IIFactors of 10: 1, 2, 5, 10.

IIIStep 2: List all the factors of 15.

IVFactors of 15: 1, 3, 5, 15.

VStep 3: Identify the numbers that appear in both lists.

VIThe numbers common to both lists are 1 and 5.

Answer

The common factors of 10 and 15 are 1 and 5.

Common mistakes

✗Confusing factors with multiples (e.g., listing multiples when asked for factors).
✗Missing some factors when listing them (e.g., forgetting 1 or the number itself).
✗Not checking all possible divisions when finding factors.
✗Making multiplication errors when listing multiples.

Exam tips

★Learn your multiplication tables (tables up to 10 or 12 are very helpful).
★When finding factors, be systematic: start from 1 and go upwards, checking each number.
★Always double-check your calculations for both factors and multiples.
★Practice regularly to become quick and accurate in identifying factors and multiples.

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