(5) Five

Divisibility by 5

  • If the digit at the unit place is either 0 or 5 then the number is divisible by 5 else not.

Proof, How: Divisibility by Five

Let the number be abcd.

abcd can be written as
a×1000 + b×100 + c×10 + d

which can also be written as
a×5×200 + b×5×20 + c×5×2 + d

Every power of 10 i.e. 10x is divisible by 5, where x is an integer.

So a×5×200 + b×5×20 + c×5×2 is divisible by 5 as it has 5 as factor or common factor.

The number is divisible by 5 if the last digit is 5 or zero.

Remainder on division by 5

  1. The remainder is the last digit (if last digit < 5) and (last digit - 5) (if the last digit > 5).

Examples of division by 5

  1. Is 340 divisible by 5.
    The last digit is 0 hence the number is divisible by 5.

  2. Is 3483 divisible by 5.
    The remainder is the last digit (if last digit < 5) and (last digit - 5) if the last digit > 5. As it is less than 5 therefore the remainder is the last digit i.e. 3.

  3. Is 377 divisible by 5.
    The remainder is the last digit (if last digit < 5) and (last digit - 5) if the last digit > 5.As it is greater than 5 therefore the remainder is the (last digit - 5) i.e. (7-5) = 2.
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