Divisibility Rule of 10


 
 
Concept Explanation
 

Divisibility Rule of 10

Divisibility Rule of 10:

A number is divisible by 10, if its units digit is zero.

Justification:

Let ...cba be an arbitrary number whose ones digit is a, tens digit is b, hundreds digit is c and so on. Then,

               overline{...cba}=...+100c+10b+a

Rightarrow ;;;;overline{...cba}=10(...+10c+b)+a

Rightarrow ;;;;overline{...cba}=10k+a,;where;k;=...+10c+b

Rightarrow ;;;;overline{...cba} is divisible by 10 if and only if a = 0.

Rightarrow ;;;;overline{...cba} is divisible by 10 if and only if its units digit is 0.

It follows from the above discussion that a number is divisible by 10 if and only if its units digit is zero.

Hence the Test of Divisibility By 10 that is a number is divisible by 10, if its units digit is zero is justified

Illustration 1:  Write 231 in the form 10b + a then check its divisibility by 10

Solution: We will express 231 in the form 10b + a

Rightarrow ;;231=10times 23+1

Rightarrow ;;231=10b+a,   where a = 1 and b = 23.

The number 231 will leave a remainder 1 when divided by 10 because the digit at the unit place represented by a in general form is 1.

Sample Questions
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Question : 1

Which of the following number is divisible by 10 ?

652360, 435764, 678576, 365460, 456737, 3457478

Right Option : D
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Explanation
Question : 2

The value of literal b is ______ when 236 in the form 10b + a and the remainder when 236 is divided by 10 is ____________.

Right Option : B
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Explanation
Question : 3

Which of the follwoing numbers is not divisible by 10

Right Option : D
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Explanation
 
 


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