Session 2: What is a Multiple? – Definition, Properties, Interactives and Examples

Arithmetic is that branch of mathematics that focuses on numbers and various operations performed on them. While discussing operations such as multiplication and division, we often come across terms like factors and multiples. These two terms are directly related to one another.

In this section, we will learn how factors and multiples are related and differentiated from each other. 

What are Multiples?

Factors and multiples are related to each other. A factor is a number that divides another number completely without any remainder, while a multiple is a product that is obtained when one number is multiplied by another number.

In general, if ab=c, where  then a and b are factors of c. The product c  is called a multiple of a and b.

Here are some multiples of 3, multiplied by different natural numbers.

Listing out these products is the same as listing out multiples.

3,6,9,12,15,18…

The three dots or ellipsis at the end mean that these multiples can go on and on. 

We can say that when a number divides another number exactly, then the dividend is called a multiple of the divisor.

We know that 6 divides 12 exactly.

∴ 12 is a multiple of 6.

We also know that 2×3=6.

∴ 6 is a multiple of 2 and 3.

Properties of Multiples

Multiples of a number have certain properties. Given below are the properties of multiples: 

Property 1: Every number is a multiple of 1. 

We know that 1 is a factor of every number. 

∴ Every number is a multiple of 1. 

Thus multiples of 1 are 1, 2, 3, 4, …. 100, 101, 102, ……

Property 2: Every multiple of a non-zero number is either greater than or equal to the given number. 

All the multiples of 7 are 7, 14, 21, 28, 35, 42, …

Clearly, each of them is greater than or equal to 7. 

Property 3: Every non-zero number is a multiple of itself. 

We have 

5=5×1
19=19×1
23=23×1  and so on

So, every number is the smallest multiple of itself.  

Property 4: Every non-zero number has infinite multiples. 

Multiples of 10 are 10, 20, 30, ……., 100, 110, ……., 1000, ……. 10000, …..

Clearly, 10 has infinite multiples. 

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What is a Multiple? – Examples

Example 1

List out the first seven multiples of 6.

The first seven multiples of 6 are 6, 12, 18, 24, 30, 36, 48.

Remember this!

• A factor is a number that divides another number completely without any remainder. 
• A multiple is a product obtained when one number is multiplied by another number. 
• Every number is a multiple of 1. 
• Every multiple of a non-zero number is either greater than or equal to the given number. 
• Every non-zero number is multiple in itself. 
• Every non-zero number has infinite multiples.