Multiples in Mathematics

In mathematics, Multiples are what we get after multiplying the number by an integer like 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...(not a fraction).
The product of any quantity and an integer are known as Factors. In other words, for the quantities a and b, we say that b is a multiple of a  if  b = na for some integer n like 0, 1, 2, 3, 4, ..., which is called the multiplier If a is not zero, this is equivalent to saying that b/a is an integer since the division of zero is not possible.
The above definition can be also written in many ways like:-
' On  Multiplying numbers the obtained product is called a multiple of that numbers such as 2 x 3 = 6 so 6 is multiple of 2 as well as 3 also'
The Multiples of any number are always greater than or equals to given Numbers and it is different from Factors. Multiples also not to be confused with multiplication generally.

Anyone can write multiples easily with the help of Their tables in such a way ( Here i am writing few examples of multiples like 1, 2, 3, 5, 6, 10, 100, ... ) :-

Multiples of 1

• 1 × 0 = 0, so 0 is a multiple of 1
• 1 × 1 = 1, so 1 is a multiple of 1
• 1 × 2 = 2, so 2 is a multiple of 1
• 1 × 3 = 3, so 3 is a multiple of 1
• 1 × 4 = 4, so 4 is a multiple of 1
• 1 × 5 = 5, so 5 is a multiple of 1
• 1 × 6 = 6, so 6 is a multiple of  1
• 1 × 7 = 7, so 7 is a multiple of 1
• 1 × 8 = 8, so 8 is a multiple of 1
• 1 × 9 = 9, so 9 is a multiple of 1
• 1 × 10 = 10, so 10 is a multiple of 1 
• and so on

Multiples of 2

• 2 × 0 = 0, so 0 is a multiple of 2
• 2 × 1 = 2, so 2 is a multiple of 2
• 2 × 2 = 4, so 4 is a multiple of 2
• 2 × 3 = 6, so 6 is a multiple of 2
• 2 × 4 = 8, so 8 is a multiple of 2
• 2 × 5 = 10, so 10 is a multiple of 2
• 2 × 6 = 12, so 12 is a multiple of  2
• 2 × 7 = 14, so 14 is a multiple of 2
• 2 × 8 = 16, so 16 is a multiple of 2
• 2 × 9 =  18, so 18 is a multiple of 2
• 2 × 10 = 20, so 20 is a multiple of 2 
• and so on

Multiples of 3

• 3 × 0 = 0, so 0 is a multiple of 3
• 3 × 1 = 3, so 3 is a multiple of 3
• 3 × 2 = 6, so 6 is a multiple of 3
• 3 × 3 = 9, so 9 is a multiple of 3
• and so on

Multiples of 5

• 5 × 0 = 0, so 0 is a multiple of 5
• 5 × 1 = 5, so 5 is a multiple of 5
• 5 × 2 = 10, so 10 is a multiple of 5
• 5 × 3 = 15, so 15 is a multiple of 5
• 5 × 4 = 20, so 20 is a multiple of 5
• 5 × 20 = 100, so 100 is a multiple of 5
• 5 × 30 = 150, so 150 is a multiple of 5
• 5 × 400 = 2000, so 2000 is a multiple of 5
• and so on

Multiples of 6

it is not necessary to start from 0 or 1 or 2 or 3 etc , we can write according to our choice.

• 3 × 6 = 18, so 18 is a multiple of 6
• 4 × 6 = 24, so 24 is a multiple of 6
• 5 × 6 = 30, so 30 is a multiple of 6
• 6 × 6 = 36, so 36 is a multiple of 6
• and so on

Multiples of 10

• 10 × 0 = 0, so 0 is a multiple of 10
• 10 × 1 = 10, so 10 is a multiple of 10
• 10 × 2 = 20, so 20 is a multiple of 10
• 10 × 3 = 30, so 30 is a multiple of 10
• 10 × 4 = 40, so 40 is a multiple of 10
• 10 × 5 = 50, so 50 is a multiple of 10
• 10 × 6 = 60, so 60 is a multiple of  10
• ( intentionally I left 70 , which is also multiple)
• 10 × 8 = 80, so 80 is a multiple of 10
• 10 × 9 = 90, so 90 is a multiple of 10
• 10 × 10 = 100, so 100 is a multiple of 10 
• and so on 

We can write multiples of any number in mathematics up to any time according to our requirements.

Multiples of 100

• 100 × 0 = 0, so 0 is a multiple of 100
• 100 × 1 = 100, so 100 is a multiple of 100
• 100 × 2 = 200, so 200 is a multiple of 100
• 100 × 3 = 300, so 300 is a multiple of 100
• 100 × 4 = 400, so 400 is a multiple of 100
• 100 × 5 = 500, so 500 is a multiple of 100
• 100 × 6 = 600, so 600 is a multiple of  100
• 100 × 7= 700, so 700 is a multiple of 100
• 100 × 8 = 800, so 800 is a multiple of 100
• 100 × 9 = 900, so 900 is a multiple of 100
• 100 × 10 = 1000, so 1000 is a multiple of 100 
• 100 × 18 = 1800, so 1800 is a multiple of 100
• 100 × 90 = 9000, so 9000 is a multiple of 100
• 100 × 100 = 10000, so 10000 is a multiple of 100
• and so on we can write so many times...

Basic Properties of Multiples

(1)   0  ( Zero) is a multiple of every number. 

Such as:-

• 1 × 0 = 0, so 0 is a multiple of 1
• 2 × 0 = 0, so 0 is a multiple of 2
• 3 × 0 = 0, so 0 is a multiple of 3
• 10 × 0 = 0, so 0 is a multiple of 10

(2) Every number is a multiple of 1 ( One). 

Such as:-

• 1 × 0 = 0, so 0 is a multiple of 1
• 1 × 1 = 1, so 1 is a multiple of 1
• 1 × 2 = 2, so 2 is a multiple of 1
• 1 × 3 = 3, so 3 is a multiple of 1  etc    

(3)  Multiples of a number are always infinite (we can write to them easily).

Such as:-

• 100 × 0 = 0, so 0 is a multiple of 100
• 100 × 10 = 1000, so 1000 is a multiple of 100
• 100 × 20 = 2000, so 2000 is a multiple of 100
• 100 × 18 =1800, so 1800 is a multiple of 100
• 100 × 19 = 1900, so 1900 is a multiple of 100
• 100 × 10 = 1000, so 1000 is a multiple of 100 
• 100 × 18 = 1800, so 1800 is a multiple of 100
• 100 × 90 = 9000, so 9000 is a multiple of 100
• 100 × 1000 = 100000, so 100000 is a multiple of 100

and so on we can write so many times...
(4)  The product of any two or more factors is the multiples of each factor. 
Such as:-

• 2 x 5 x 1 = 10,

       Therefore, 10 is the multiple of both 1, 2, and 5.

• 3 x 1 = 3,

       Therefore, 3 is the multiple of both 3 and 1.

• 30 = 2 x 3 x 5 x 1,

       Therefore, 30 is the multiple of 1, 2, 3 and 5.

• 36 = 2 x 2 x 3 x 3 x 1 ,

       Therefore, 36 is the multiple of 1, 2, 3, 4, 6, 9, 12, 18 and 36.

(5)  Every number is a multiple of Itself. 

Such as:-

• 1 × 1 = 1, so 1 is a multiple of 1
• 3 × 1 = 3, so 3 is a multiple of 3
• 2 × 1 = 2, so 2 is a multiple of 2
• 5 × 1 = 5, so 5 is a multiple of 5
• 10 × 1 = 10, so 10 is a multiple of 10
• 100 × 1 = 100, so 100 is a multiple of 100
• 2012 × 1 = 2012, so 2012 is a multiple of 2012
• 6666 × 1 = 6666, so 6666 is a multiple of 6666

Note :- In general, when a and b are both integers, and b is a multiple of a, then a is called a DIVISOR of b.We can also says that a divides b. 

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