# RULES OF DIVISIBILITY - FOR 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 AND PRIME DIVISORS 13 TO 47 AND ABOVE

Multiplication Tables
and
Division before Rules Of Divisibility
They are prerequisites here.

Here we study methods that can be used to determine
whether a number is evenly divisible by other numbers.

These are shortcuts for testing a number's factors
without resorting to division calculations.

The rules given below transform a given number's divisibility
by a divisor to a smaller number's divisibility by the same divisor.

If the result is not obvious after applying it once,
the rule should be applied again to the smaller number.

We present the rules with examples, in a simple way,
to follow, understand and apply.

We provide the rules for all the single digit divisors
and prime divisors upto 47 and above
and a general method which is simple to use.

## Rules Of Divisibility for 2 and 4

Given below is the Link for
Divisibility Rules for 2 and 4.

Divisibility by 2 and 4

## Rules Of Divisibility for 3 and 6

Given below is the Link for
Rules Of Divisibility for 3 and 6.

Divisibility by 3 and 6

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## Rules Of Divisibility for 5 :

A number is divisible by 5, if its last digit (units' digit) is either 0 or 5.

Examples:

5342 is not divisible by 5, since last digit is neither 0 nor 5.
4235 is divisible by 5, since last digit is 5.

2345 is divisible by 5, since last digit is 5.
7530 is divisible by 5, since last digit is 0.

3075 is divisible by 5, since last digit is 5.
3057 is not divisible by 5, since last digit is neither 0 nor 5.

5120 is divisible by 5, since last digit is 0.
5012 is not divisible by 5, since last digit is neither 0 nor 5.

98760 is divisible by 5, since last digit is 0.
67453 is not divisible by 5, since last digit is neither 0 nor 5.

Given below are the Links for
Rules Of Divisibility for 7 and 8.

Divisibility by 7

Divisibility by 8

## Rules Of Divisibility for 10 :

A number is divisible by 10, if its last digit (units' digit) is 0.

Examples:

The numbers 70, 900, 5680, , 20000, 37610
are divisible by 10 as all have the last digit 0.

The numbers 97, 121, 5008, 98761, 605009
are not divisible by 10, as they do not have 0 in the units' place.

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## Rules Of Divisibility for 9 :

A number is divisible by 9, if the number obtained by adding its digits is divisible by 9.
If you don't know the new number's divisibility, you can apply the rule again. (usually, it is not required to apply again.)

Example 1 of Divisibility Rule for 9

Find whether 23454 is divisible by 9 or not.

Solution :
The number formed by sum of the digits = 2 + 3 + 4 + 5 + 4 = 18.
We know 18 is divisible by 9.
∴ 23454 is divisible by 9. Ans.

Example 2 of Divisibility Rule for 9

Find whether 641857 is divisible by 9 or not.

Solution :
The number formed by sum of the digits = 6 + 4 + 1 + 8 + 5 + 7 = 31.
We know 31 is not divisible by 9.
∴ 641857 is not divisible by 9. Ans.

Example 3 of Divisibility Rule for 9

Find whether 652743 is divisible by 9 or not.

Solution :
The number formed by sum of the digits = 6 + 5 + 2 + 7 + 4 + 3 = 27.
We know 27 is divisible by 9.
∴ 652743 is divisible by 9. Ans.

Example 4 of Divisibility Rule for 9

Find whether 5230716 is divisible by 9 or not.

Solution :
The number formed by sum of the digits = 5 + 2 + 3 + 0 + 7 + 1 + 6 = 24.
We know 24 is not divisible by 9.
∴ 5230716 is not divisible by 9. Ans.

Example 5 of Divisibility Rule for 9

Find whether 91451087 is divisible by 9 or not.

Solution :
The number formed by sum of the digits = 9 + 1 + 4 + 5 + 1 + 0 + 8 + 7 = 36.
We know 36 is divisible by 9.
∴ 91451087 is divisible by 9. Ans.

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## Rules Of Divisibility 11 and Prime Divisors up to 47 and above.

Given below are the Links for
Divisibility Rules for 11 and Prime Divisors up to 47 and above.

Divisibility by 11

Divisibility Test for 2 to 11

Divisibility by Prime Divisor

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