Divisibility Rule of 9


 
 
Concept Explanation
 

Divisibility Rule of 9

Divisibility Rule of 9:

A number is divisible by 9, if the sum of its digits is divisible by 9.

Justification:

Let us first consider case of a two digit number:

 n=overline{ab} be a two digit number. Then, n can be written as

         n = 10a + b, where b is units digit of n.

Rightarrow    n = 9a + a + b

Rightarrow    n = a multiple of 9 + ( a + b )

Rightarrow    n is a multiple of 9, if ( a + b ) is a multiple of 9

Thus, a two digit number is divisible by 9, if the sum of its digits is divisible by 9.

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Sample Questions
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Question : 1

Replace by a  digit so that the number is divisible by 9.

1______ 80498

Right Option : B
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Question : 2

If overline{24a} is divisible by 9, the value of a is ___________.

 

Right Option : B
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Question : 3

A 6 digit number begins with the digit 8. The number is divisible by 9. All the digits of the number are different. What is the smallest possible value of this number?

Right Option : B
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Explanation
 
 


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