# Multiple of 9

### What is A Common Multiple?

A common multiple is defined as a number that is a multiple of two or more numbers in a given set. Let us understand through an example.

Let us take  two numbers 15 and 30

Common multiples of 15 are 14,30,45,60,75,90

Common multiples of 30 are 30, 60, 90, 120,150,180

Here, we can see 30 and 60 are the first two common multiples of 15 and 30.

### What is a Factor?

A number will only be considered as a factor of any other second number if it divides the second number completely without leaving any remainder. In other words, if a number( dividend) is completely divisible by any other number ( divisor) then the divisor is said to be a factor of that dividend.

For example, 9 is a factor of 27 i.e. 9 divides 27 exactly giving quotient as 3 and leaving zero as remainder.

### How to Find Multiples Using Multiplication?

We can find multiples by multiplying the number with any integer.

 Examples showing the multiples of 9   Multiply 9 by 1, then by 2, then by 3 and so on.   9*1= 9, 9*2 =18, 9*3 =27, 9* 4 =36, 9*5= 45,9*6=54   Hence, the first 6 multiples of 9 aree 9, 18, 26, 36, 45, 54

How to Find Multiple Using Division?

As we know, both multiplication and division are inverse operations. It implies both are linked with each other. We can find out using division whether a given number is multiple of another number or not.

### Some of The Examples Are Mentioned Below:

1. 27÷ 9 = 3, so 27 can be divided evenly by 9 and is also a multiple of 9. Since, 3 * 9= 27.

2. 18 ÷ 2 = 9, s0 18 can be divided by 3 and is also a multiple of 3. Since, 9 * 2= 18

### Some of the multiples of 9 are

 9 39 27 63 81

### Any number that can be represented as in the form of 9n, where n is considered as an integer and a multiple of 9. So, if two values x and y are there, we can say that y is a multiple of x if y = nx for some integer n.

For example, 90, 72, 27, and 900 are all multiples of 9

 90 = 9 x 10 72 = 9 x 8 27 = 9 x 3 900 = 9 x 100

These values are known as multiple as we received these values by adding and subtracting the original value several times.

## List of the multiples of 9

 Multiplication Multiples of 9 9 * 1 9 9 * 2 18 9 * 3 27 9 * 4 36 9 * 5 45 9 * 6 54 9 * 7 63 9 * 8 72 9 * 9 81 9 * 10 90

### Solved Examples

1. We say that these numbers are multiples of 7. Play the game by changing the number to 8. Now, which number did you replace with ‘Teddy’? These numbers are multiples of 8. Write any 10 multiples of 9.

Solution: The numbers that are replaced with’ teddy ‘are 8, 16,24, 32, 40, 48, 56, 64, 72, 80.

Ten multiples of 9 are:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

2.    Write any 6 multiples of each of the following:

1.      15

2.      11

3.      12

4.      13

Solution:

1.      The six multiples of 15  are- 15,30,45,60,75,90

2.      The six multiples of 11 are – 11, 22, 33, 44, 55, 66

3.      The six multiples of 12 are- 12,24,36,48,60,72

4.      The six multiples of 13 are 13, 26, 39, 52, 65, 78

Quiz Time

1.  What are the multiples of a 16 between 40 and 90/

1. 48,64,80

2. 44,64,80

3. 42,66,86

4. 46,68,88

2.  Which one of the following is a multiple of 2 but not a factor of 8?

1. 2

1. 8

2. 4

3. 6

3.  What is the seventh multiple of 9 ?

1. 81

2. 56

3. 45

4. 63