Divisibility Rules

A very old mathematical operation called DIVISION OF NUMBERS that we are doing from our childhood but we don't understand it clearly and also we don't know how to do it properly and what are it's applications. Let's see how much you know about division of numbers.

I will divide the article in 3 parts:
  • When we divide a number by another number then we have 4 terms
  • There can be two cases in the division of two numbers 
  • Two important application of remainders
(1) When we divide a number by another number then we have 4 defined terms namely:
  1. Divisor or Factor
  2. Dividend
  3. Quotient 
  4. Remainder
Now you should know the meaning of these terms and also where they are in a division process. I want you to look at this picture. All the 4 terms are placed in their respective places.
Divisibility Rules for SSC CGL/CHSL/MTS
Credits: flatworldknowledge.com

1. Divisor: A number that is going to divide the the dividend.

2. Dividend: Whose division is going to happen.

3. Quotient: The parts in which the dividend is divided.

4. Remainder: Number whose division is not possible by the respective divisor.

Now there is a relation between these 4 terms and that is:


27 = (5 X 5) + 2
33 = (4 X 8) + 1
54 = (7 X 7) + 5

In the above given examples
  • Dividend = 27, 33 and 54
  • Divisor or Factor = 5, 4 and 7
  • Quotient = 5, 8 and 7
  • Remainder = 2, 1 and 5
[NOTE: Quotient and Remainder always come out as WHOLE NUMBERS (0,1,2,3,4.....)]

(2) There can be two cases in the division of two numbers either the:
  1. Remainder will be ZERO or
  2. Remainder will come out as any other whole number but not zero (remember it can never be a negative integer)
When remainder is zero

In the division of two numbers when the remainder becomes zero the we say that the DIVIDEND is divisible by DIVISOR.

So for instance what is the remainder in 36 / 6 ?

36 = (6 X 6) + 0

As the remainder becomes zero we will say that 36 is divisible by 6. 

When the remainder is any other whole number other than zero

Of course then we will say that the DIVIDEND is not divisible by DIVISOR. For Instance 

27 = (5 X 5) + 2 (27 is not divisible by 5, it leaves remainder 7)
33 = (4 X 8) + 1 (33 is not divisible by 4, it leaves remainder 1)

(3) Two applications of Remainders

1. Making the dividend divisible to divisor 

Now 27 is a dividend and when we try to divide it by 5 it leaves remainder 2.

Now the meaning of remainder is what cannot be divisible by the particular divisor.

That means if we subtract the remainder from the dividend the resultant number will become divisible by the given divisor. Let's try.

Dividend - Remainder

27 - 2 = 25  (Now it is divisible by 5 as the INDIVISIBLE PART is removed)

33 - 1 = 32 (Now it is divisible by 5 as the INDIVISIBLE PART is removed)

2. Making the divisor able to divide the dividend

Now when the dividend was not divisible by the divisor we did one thing and that was removing the indivisible part so that it becomes a number divisible by the divisor.

There is also another method in which we make changes to the divisor. It goes like this
  • Getting the difference of Divisor and Remainder 
  • Adding this Difference to the Divisor so that the resultant number can divide the Dividend.

27 = (5 X 5) + 2

Difference of Divisor and Remainder: 5 - 2 = 3

Adding this to the Dividend: 27 + 3 = 30 (Now it is divisible by 5).

Divisibility Series:

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