GRADE 6 · MATHEMATICS

Factors, Multiples, HCF and LCM

Factors and multiples help us understand how numbers are built and how they relate to one another. Learn prime and composite numbers, find common factors and multiples, and calculate the highest common factor (HCF) and lowest common multiple (LCM).

Learning time: approximately 30 minutes · Beginner level

What You Will Learn

Identify factors and multiples of a number.
Recognise prime and composite numbers.
Find common factors and the HCF.
Find common multiples and the LCM.
Use HCF and LCM in simple problems.

1. What Is a Factor?

A factor is a whole number that divides another number exactly, with no remainder.

Example: Factors of 12

1 × 12 = 12, 2 × 6 = 12 and 3 × 4 = 12.

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

Factors come in pairs. Every whole number greater than zero has at least two positive factors: 1 and itself.

2. What Is a Multiple?

A multiple is the result of multiplying a number by a whole number. The multiples of 4 are 4, 8, 12, 16, 20, 24 and so on.

Number	First five positive multiples
3	3, 6, 9, 12, 15
5	5, 10, 15, 20, 25
7	7, 14, 21, 28, 35

Do not mix them up: Factors divide a number exactly. Multiples are found by multiplying the number.

3. Prime and Composite Numbers

A prime number has exactly two positive factors: 1 and itself. A composite number has more than two positive factors.

2, 3, 5, 7 and 11 are prime.
4, 6, 8, 9 and 12 are composite.
1 is neither prime nor composite because it has only one positive factor.

Special fact: 2 is the only even prime number. Every other even whole number greater than 2 is composite.

4. Common Factors and Highest Common Factor (HCF)

Common factors are numbers that divide each of two or more numbers exactly. The highest common factor is the largest of those common factors.

Worked example: Find the HCF of 12 and 18

Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 18: 1, 2, 3, 6, 9, 18.
Common factors: 1, 2, 3 and 6.
The greatest common factor is 6.

5. Common Multiples and Lowest Common Multiple (LCM)

Common multiples are numbers that appear in the multiples of each number. The lowest common multiple is the smallest positive common multiple.

Worked example: Find the LCM of 4 and 6

Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
The first positive common multiple is 12.

LCM = 12.

6. When Do We Use HCF and LCM?

Use HCF when you want to split or group things into the largest equal groups without leftovers.
Use LCM when events repeat and you want to find when they happen together again.

HCF example: You have 12 red counters and 18 blue counters. The largest number of identical groups you can make, using all counters with the same number of each colour in every group, is 6 groups.

LCM example: One bell rings every 4 minutes and another every 6 minutes. If they ring together now, they will next ring together in 12 minutes.

7. Common Mistakes to Avoid

Calling a multiple a factor: A factor divides exactly; a multiple is made by multiplying.

Calling 1 a prime number: A prime number has exactly two positive factors. The number 1 has only one.

Choosing a large common multiple for LCM: LCM means the smallest positive common multiple.

Choosing a small common factor for HCF: HCF means the greatest common factor.

8. Practice Exercises

Try these before revealing the answers.

List all positive factors of 10.
Write the first five positive multiples of 6.
Is 17 prime or composite?
Find the HCF of 8 and 12.
Find the LCM of 3 and 5.
Find the HCF of 15 and 25.
Find the LCM of 4 and 10.
Two lights flash every 5 seconds and every 8 seconds. If they flash together now, after how many seconds will they next flash together?

Show practice answers and explanations

1, 2, 5 and 10.
6, 12, 18, 24 and 30.
Prime; its only positive factors are 1 and 17.
Common factors are 1, 2 and 4, so HCF = 4.
First common multiple is 15, so LCM = 15.
Common factors include 1 and 5, so HCF = 5.
Multiples of 4: 4, 8, 12, 16, 20; multiples of 10: 10, 20. LCM = 20.
LCM of 5 and 8 is 40, so they next flash together after 40 seconds.

10. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

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