Page 50 - Maths Class 05

3 Multiples and Factors

Looking Back

A factor is a number which divides another number without leaving a remainder.
For example : 14 ÷ 2 = 7, 14 ÷ 7 = 2

2 and 7 are factors of 14, because 2 × 7 = 14

A number can have many factors.

Example : What are the factors of 12 ?

Solution : 3 and 4 are factors of 12, because 3 × 4 = 12.
Also, 2 × 6 = 12. So, 2 and 6 are also factors of 12.

And, 1 × 12 = 12. So, 1 and 12 are factors of 12 as well.

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

Multiples

In the process of multiplication we see that 12 × 9 = 108. Here, 108 is called the product
of 12 and 9 and in other words it is also said that 108 is the multiple of 12 and 9.

In multiplication table of any number, the product of the number and a counting
number is called the multiple of both the numbers.

For example : 16 × 1 = 16

16 × 2 = 32

16 × 3 = 48

In the above example, 16, 32, 48... are the multiples of 16.
Properties of Multiples

« ‘0’ is a multiple of every number.
« The smallest multiple of a number (except zero) is the number itself.

« There is nothing like the greatest or the last multiple of a number.

« Every number is a multiple of 1.

« Multiples of a whole number are either equal or greater than the number.

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