Divisibility Rule of 5


 
 
Concept Explanation
 

Divisibility Rule of 5

Divisibility Rule of 5:

 A number is divisible by 5, if its units digit is 0 or 5.

Justification:

Let n be any natural number. Then, n can be written as

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

Clearly, 10 is a multiple of 5. Therefore, 10a is also a multiple of 5.

The sum of any two multiples of 5 is a multiple of 5. Therefore, 10a+b will be a multiple of 5, if b is a multiple of 5.

Thus, an integer is divisible by 5, if its units digit is a multiple of 5. That is its units digit is either 0 or 5.

Hence the Test of Divisibility By 5 that is a number is divisible by 5, if its units digit is 0 or 5 is justified.

This implies that if the units digit of a number is not 0 or 5, then it is not divisible by 5.

In the general form since 10a is a multiple of 5. Therefore , when 10a + b is divided by 5, the remainder will be equal to the remainder when n is divided by 5.

Thus, the remainder when an integer is divided by 5 is equal to the remainder when its units digit is divided by 5.

Illustration :  Write 521 in the form 10b + a then check its divisibility by 5

Solution: We will express 521 in the form 10b + a

Rightarrow ;;521=10times 52+1

Rightarrow ;;521=10b+a,   where a = 1 and b = 52.

When 1 is divided by 5 it leaves a remainder as 1, So when 521 is divided by 5, the remainder is 1.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Write 7865 in the form 10b + a then check its divisibility by 5. Find the value of a and b also.

Right Option : B
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Explanation
Question : 2

Write 109 in the form 10b + a then check its divisibility by 5. Find the value of a and b also.

Right Option : D
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Explanation
Question : 3

Check which of the following numbers are divisible by 5?

638055, 89460, 75670, 98765 , 89763 , 87984 ,37987, 78966, 98750, 56780

Right Option : D
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Explanation
 
 


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