Divisibility Rule of 3


 
 
Concept Explanation
 

Divisibility Rule of 3:

Any natural number is divisible by 3 if the sum of its digits is also divisible by 3.

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 )

Since a multiple of 9 is also a multiple of 3, so

Rightarrow    n is a multiple of 9, if ( a + b ) is a multiple of 3

Thus, a two digit number is divisible by 3, if the sum of its digits is divisible by 3.

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Sample Questions
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Question : 1

Which of the following number is divisible by 3?

121 , 543 , 665 , 875

Right Option : B
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Explanation
Question : 2

If a 4 digit number A is divisible by 3, then which of the following is correct?

Right Option : A
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Explanation
Question : 3

If 5476a is divisible by 3, then what can be the value of a?

Right Option : B
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Explanation
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