What is Divisibility?

What do you understand by divisibility? Well, it is really very simple. If you divide a number by another, and the result is a whole number, the number is divisible by the other. If you divide the two numbers, and get a remainder, then that number is NOT divisible by the other. Here’s an example

Suppose you divide 8 by 2. What is the result? It is 4. Are there any remainders after the division? No. Then, 8 IS divisible by 2.

But what if I divide 8 by 3 instead? You would get 2 as a quotient and 2 as a remainder! So, 8 is NOT divisible by 3!

How Do I Find Out If A Bigger Number Is Divisible By Another?

The examples above consisted of a single number only! But what if you have a number that is like 288? Do you sit and divide them? No, you don’t. There are simple steps that can tell you if a number is divisible by another. Take a look at them:

Let us take up an example. Consider the number 150. Let us find out if it is divisible by the other numbers:

• 150 is divisible by 2 because the last digit is 0.
• 150 is divisible by 3 because when we add the digits (1+5+0), we get 6 which is divisible by 3.
• 150 is NOT divisible by 4, since the last 2 numbers i.e., 5 and 0 are not divisible by 0.
• 150 is divisible by5 because the last digit is 0
• 150 is divisible by 6 because it is divisible by both 2 and 3
• 150 is not divisible by 7 because when we double 0 we get o again. If we subtract that from 15, we get 15, which is not divisible by 7.
  
• 150 is not divisible by 8 because the three digits 1, 5 and 0are not divisible by 8.
• 150 is NOT divisible by 9 because the sum of the digits 1+5+0=6, which is not divisible by 9.
• 150 is divisible by 10 because the last digit is 0.

Divisibility rules are very simple. Just make sure that you practice them for at least 10 minutes every day. You will soon be the new found genius in class and your teachers will be amazed by the speed you’ve developed!

Further Tips on Divisibility:

(i) A number divisible by 2 or 5

Any number ending in 0 or an even number is divisible by 2 e.g. 12, 256, 328, 2060. If the last digit of a number is 0 or 5, that number is divisible by 5 e.g. 150, 2025, 3175.

(ii) A number divisible by 4 or 25

Any number is divisible by 4 if the last two digits are divisible by 4, e.g. 132, 5276, 208. Similarly if the last two digits of a number are divisible by 25, that number is divisible by 25, e.g. 1375, 2500.

(iii) A number divisible by 8 or 125

For a number to be divisible by 8, its last three digits must be divisible by 8, e.g. 864, 1248, 3000. Similarly numbers ending with the last three digits divisible by 125 are divisible by 125, e.g. 4250, 12375, 12000.

(iv) A number divisible by 16 or 625

A number having its last four digits divisible by 16, will be divisible by 16, e.g. 31776, 28528. Similarly numbers having their last four digits divisible by 625 are divisible by 625, e.g. 83125, 125000.

(v) A number divisible by 3 or 9

If a number is divisible by 3, the sum of the digits is divisible by 3, e.g. 38451, 285612.
In the above numbers, sum of digits 3+8+4+5+1 = 21 and 2+8+5+6+1+2 = 24, which are all divisible by 3. Hence, the numbers are divisible by 3.

In a similar manner, a number is divisible by 9, if the sum of all its digits is divisible by 9, e.g. 1548, 653229.

In the above numbers, the sum of digits = 1+5+4+8 = 18, 6+5+3+2+2+9 = 27. Hence, the numbers are divisible by 9

(vi) A number divisible by 11

A number is divisible by 11 if the difference between the sum of the digits in the even places and the sum of the digits in the odd places is either 0 or a number divisible by 11, e.g. 65274, 538472.

In 65274, difference in the sum of numbers in the odd places and the sum of numbers in the even places = (6+2+4) – (5+7) = 0

In 538472, difference in the sum of numbers in the odd places and the sum of numbers in the even places = (5+8+7) – (3+4+2) = 20 – 9 = 11, a multiple of 11.
Hence the two numbers are divisible by 11