# Multiple of 9

If we get a number by multiplying it with an integer, the resulting number is called a multiple. For example, if the number 12 is multiplied by an integer, say 4, the resulting number 48 is a multiple of 12. The numbers, though obtained, can be whole numbers or even fractional numbers. We get multiples because of multiplication and division. Addition and subtraction do not give us multiples of a number.

## Common Multiple

Any common number between two or more numbers is known as a common multiple of those numbers. For example, consider number 36. 36 comes in the table of 3, 4, 9 and 12. Therefore, we can say number 36 is a common multiple of 3, 4, 9 and 12.

## Factor

If a number divides a number completely, leaving no remainder, then the first number is a factor of the second number. For example, 12 divides 36 completely without leaving any remainder. This implies, number 12 is a factor of 36.

## Multiples of 9

We can find multiples of 9 if we multiply number 9 by any integer. For example, multiples of 9 are:
9 x 1 = 9
9 x 2 = 18
9 x 3 = 27
9 x 4 = 369 x 5 = 45 … and so on

We can get multiples of 9 by division as well. Consider the number 180. If we divide 180 by 9, we get 20. This means 180 is a multiple of 9. We must make sure that the number is completely divisible by 9, leaving no remainder.

## Some multiples of 9 are:

 9 x 1 9 9 x 2 18 9 x 3 27 9 x 4 36 9 x 5 45 9 x 6 54 9 x 7 63 9 x 8 72 9 x 9 81 9 x 10 90 9 x 11 99 9 x 12 108 9 x 13 117 9 x 14 126 9 x 15 135 9 x 16 144 9 x 17 153 9 x 18 162 9 x 19 171 9 x 20 180 9 x 21 189 9 x 22 198 9 x 23 207 9 x 24 216 9 x 25 225 9 x 26 234 9 x 27 243 9 x 28 252 9 x 29 261 9 x 30 270

## Tips for finding multiples of 9

1. If two numbers are multiples of 9, then their difference will be 9. If their difference is not 9, then they are not the multiples of 9.
2. The numbers which are divisible by 3 and 6 both, those numbers will be multiples of 9. For example, 72 is divisible by both 3 and 6. Therefore, 72 is a multiple of 9. However, some numbers may follow the condition but may not be a multiple of 9. For example, 48 is divisible by both 3 and 6, but not 9. Hence, 48 is not a multiple of 9.
3. If the sum of digits of a number is divisible by 9, then the number will be a multiple of 9. For example, consider the number 812574. The sum of its digits is 27, and 27 is divisible by 9. Hence, number 812574 is a multiple of 9.

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