Factors and multiples - 7

Multiples of a number

Up till now we have discussed finding factors of a number i.e. to find building blocks that can be used to form the given number.

Similarly, the given number can be used to form bigger numbers. So, what are such bigger numbers called as? Such numbers are called as ‘Multiples’.

In this post, we are going to discuss more about multiples.

To understand what is meant by multiples, let’s take an example.

Let the given number be 12.

12 x 1	=	12
12 x 2	=	24
12 x 3	=	36
12 x 4	=	48
.	.	.
.	.	.
.	.	.
12 x 10	=	120
12 x 11	=	132
12 x 12	=	144
.	.	.
.	.	.
.	.	.
12 x 30	=	360
.	.	.
.	.	.
.	.	.
12 x 45	=	540
.	.	.
.	.	.
.	.	.

When the given number is multiplied by a whole number, the result obtained is called a multiple of the given number.

Hence the numbers obtained in the above table lists the multiples of 12. e.g. 12, 24, 36, 48, 120, 132, 144, 360, 540 and so on are the multiples of 12.

By looking at the table above, a question arises. How many multiples a number can have?

The answer is – ‘A number can have infinite number of multiples’.

To find a multiple of a number, simply multiply the given number by a whole number. Let’s take some more examples.

Write multiples of 9:

9 x 5	=	45
9 x 13	=	117
9 x 27	=	243

 Write multiples of 15:

15 x 4	=	60
15 x 11	=	165
15 x 17	=	255

 Write multiples of 21:

21 x 6	=	126
21 x 9	=	189
21 x 12	=	252

From the above examples, you can observe that the tables of various numbers that we learnt in earlier classes are examples of multiples of those numbers.

One more interesting fact of multiples is that "0 is a multiple of all the numbers". Remember that the result of any number multiplied by 0 is always 0. 

3 x 0	=	0
26 x 0	=	0
135 x 0	=	0

Practice time:

Find the 5 multiples each of the following numbers: 

i	3
ii	4
iii	8
iv	11
v	13
vi	18
vii	22
viii	27
ix	30
x	35

Factors and multiples - Answers

Factors and multiples – 6

Find the HCF:

i	HCF of 20 & 45	=	5
ii	HCF of 16 & 56	=	8
iii	HCF of 25 & 90	=	5
iv	HCF of 48 & 108	=	12
v	HCF of 42, 70	=	14
vi	HCF of 24 & 57	=	3
vii	HCF of 60 & 70	=	10
viii	HCF of 81 & 117	=	9

Factors and multiples – 5

 List the factor pairs of the given number:

 

i	54	=	1 x 54		ii	63	=	1 x 63
		=	2 x 27				=	3 x 21
		=	3 x 18				=	7 x 9
		=	6 x 9
iii	75	=	1 x 75		iv	87	=	1 x 87
		=	3 x 25				=	3 x 29
		=	5 x 15
v	99	=	1 x 99		vi	128		1 x 128
		=	3 x 33					2 x 64
		=	9 x 11					4 x 32
								8 x 16
vii	144	=	1 x 144
		=	2 x 72
		=	3 x 48
		=	4 x 36
		=	6 x 24
		=	8 x 18
		=	12 x 12