Divisibility Rule for 5


 
 
Concept Explanation
 

Divisibility Rule for 5

Divisibility Rule For 5: This rule is used to check whether a number is divisible by 5 or not without performing long division. Any number is divisible by 5, if its units digit is a multiple of 5. That is its units digit is either 0 or 5.

Justification: Clearly, 10 is a multiple of 5.

Therefore , 10a is also a multiple of 5.

Since 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.

Illustration: Check whether 34,780 is divisible by 5.

Solution: For this rule we just look at the last digit: 34,780. The last digit is a 0, so this number is divisible by 5.

Illustration: Check whether 13,569 is divisible by 5.

Solution:  Again, we will focus our attention on the last digit: 13,569. The last digit is a 9 which is not divisible by 5 so this number is not divisible by 5. 

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

For example, if

  •    521 is divided by 5, the remainder is 1 also the unit place digit 1 will give a remainder 1 whne divided by 5.
  •    294 is divided by 5, the remainder is 4.also the unit place digit  4 will give a remainder 4 whne divided by 5.
  •    928 is divided by 5, the remainder is equal to the remainder when 8 is divided by 5. i.e. equal to 3.
  •    2587 is divided by 5, the remainder is equal to 2.
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