Divisibility Rules | Check the divisibility of number (1 – 10)

Check the divisibility of any number- the divisibility of any number confirms you weather the number will be divided by divisor or not. To know the divisibility of any number becomes very important in order to save time in competitive examination. Divisibility can be checked within a few seconds after that you can choose which number you have to choose for dividing the number. There are some basic rules for checking number’s divisibility which we will have to follow.

Check the Divisibility by 2:

The number will be divided by 2 easily if it is even number  (unit digit is 2,4,6,8,0)

Example: 123456, 1234, 4578 are divisible by 2 because a number is even and it ends with 2,4,6,8,0.

Check the Divisibility by 3:

The number will be easily divisible by 3 if its sum of the digit is divisible by 3.

Example: 729
For checking divisibility of 729 we must add 7+2+9=18 which is also divisible by 3. So
So 729 will be divisible by 3.

Check the Divisibility with 4:

In order to check divisibility with 4, you have to only see the number’s last two digits, if last two digits of the number are divisible by 4 then you can easily say that your number will be completely divisible by 4.

Example: 7985783324
The given number is very big. If We have to check its divisibility then we have to see only its last two-digit. i.e. 24 which comes in a table of 4
So we can easily say just by saying the number is divisible by 4

Check the Divisibility with 5:

It is very simple just by seeing the number you can tell the answer to it. If the last digit is either 0 or 5 the number will be completely divided by 5

Check the Divisibility by 6:

As we know
6=3*2
So in order to check divisibility with 6 it must have a factor of 2 and 3. We can say that the number will be divisible by both 2 and 3
So if the number is even it is divisible by 2 and if it’s some of the digits is divisible by 3 then it is divisible by 3
Hence after checking it’s divisibility by 2&3 we can say that no is divisible by 3

Example: 216
The given no is even no so and its some of the digits is 9 which comes in the table of 3 so no is also divisible by 3. Hence we can say that no will be divisible by 6 also.

Check the Divisibility with 7:

We use oscillator (– 2) for divisibility test.

for example take number 39732

step 1 : Separate unit place from the given number and multiplied by “-2” for unit digit place ( 2 x -2 = -4) . This product is to be add for remaining number [ 3973 + (-4) = 3969].

step 2 : Separate unit place from 3969 and multiplied by “-2” for unit digit place ( 9 x -2 = -18) . This product is to be add for remaining number [ 396 + (-18) = 378].

step 3 : Separate unit place from 378 and multiplied by “-2” for unit digit place ( 8 x -2 = -16) . This product is to be add for remaining number [ 37 + (-16) = 21].

Here 21 is divisible by 7 so the given number is also divisible by 7

Check the Divisibility with 8:

A number is divisible by 8, if the number formed with its last three digits is divisible by 8.

Example: Take number 24344. Consider the last two digits i.e. 344. As 344 is divisible by 8, the original number 24344 is also divisible by 8.

Check the Divisibility with 9:

A number is divisible by 9, ifsum of digits of a number are divisible by 9

Example: Consider 78532, as the sum of its digits (7+8+5+3+2) is 25, which is not divisible by 9, hence 78532 is not divisible by 9

Check the Divisibility with 10:

Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

Example: 10, 20,30,1000,5000,60000 etc.

Divisor

Divisibility condition

Examples

1

No special condition. Any integer is divisible by 1.

2,3 etc

2

The last digit is even (0, 2, 4, 6, or 8)

1,294: 4 is even.

3

sum of whose digits are divisible by 3

516 = 5+1+6=12,which is divisible by 3.

4

If last two digits of number is divisible by 4.

40,832: 32 is divisible by 4.

5

The last digit is 0 or 5

405: the last digit is 5.

6

It is divisible by 2 and by 3.

1458: 1 + 4 + 5 + 8 = 18, so it is divisible by 3 and the last digit is even, hence the number is divisible by 6.

7

Form the alternating sum of blocks of three from right to left.

1,369,851: 851 − 369 + 1 = 483 = 7 × 69

Subtract 2 times the last digit from the rest. (Works because 21 is divisible by 7.)

483: 48 − (3 × 2) = 42 = 7 × 6.

Or, add 5 times the last digit to the rest. (Works because 49 is divisible by 7.)

483: 48 + (3 × 5) = 63 = 7 × 9.

Or, add 3 times the first digit to the next. (This works because 10a + b − 7a = 3a + b − last number has the same remainder)

483: 4×3 + 8 = 20 remainder 6, 6×3 + 3 = 21.

8

If last three digits of number is divisible by 8.

413984 = 984/8 = 123 , which is divisible by 8

9

sum of digits of a number are divisible by 9.

2,880: 2 + 8 + 8 + 0 = 18: 1 + 8 = 9, which is divisible by 9

10

The last digit is 0

120: the last digit is 0.

I hope, this article will help you a lot to understand the Divisibility Rules | Check the divisibility of number (1 – 10). If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.

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