Divisibility Rule for 10


 
 
Concept Explanation
 

Divisibility Rule for 10

Divisibility Rule of 10: This rule is used to check whether a number is divisible by 10 or not without performing long division.  The rule states that a number is divisible by 10 if and only if tis 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,the number can be expanded as

 ...cba = .....+100c+10b+a

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

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

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

Rightarrow ;;;; ...cba is divisibli 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 tis units digit is zero.

Illustration:  Check whether 241630.is divisible by 10.

Solution: To check whether 241630 is divisible by 10. As the digit at the unit place is 0. So the number is divisible by 10.

Illustration:  Check whether 187525.is divisible by 10.

Solution: To check whether 187525 is divisible by 10. As the digit at the unit place is 5. So the number is not divisible by 10.

 
 
 


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