## DIVISIBILITY RULES 1 TO 10

In this section, you will learn the shortcuts (rules) to check whether a number is evenly divisible by another number without doing too much calculation.

Once we remember these rules, we can do division of numbers easily without calculator.r

## Divisibility Rule for 2

All even numbers are divisible by 2.

A number  ends with one of the following digits is called as even number.

0, 2, 4, 6 or 8

## Divisibility Rule for 2 - Example

Problem :

Check whether 16 is divisible by 2.

Solution :

16 ends with the digit 6.

So, it is even number and it divisible by 2.

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## Divisibility Rule for 3

To check whether a number is divisible by 3, we have to find the sum of the digits in the number.

If the sum of the digits is divisible by 3 or multiple of 3, then the number is divisible by 3.

## Divisibility Rule for 3 - Example

Problem :

Check whether 252 is divisible by 3.

Solution :

Add all the digits in the number 252.

2 + 5 + 2  =  9

The sum of the digits in the given number 252 is 9 which is a multiple of 3.

So, 252 is divisible by 3.

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## Divisibility Rule for 4

If the last two digits of a number are zeroes or the number formed by the last 2 digits is divisible by 4, then the number is divisible by 4.

## Divisibility Rule for 4 - Example

Problem :

Check whether 328 is divisible by 4.

Solution :

In the given number 328, the last two digits are not zeroes.

But, the number formed by the last two digits is 28 which is divisible by 4.

So, the given number 328 is divisible by 4.

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## Divisibility Rule for 5

If a number ends with 0 or 5, then it is divisible by 5.

## Divisibility Rule for 5 - Example

Problem :

Check whether 105 is divisible by 5.

Solution :

The given number 105 ends with 5.

So, the given number 105 is divisible by 5.

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## Divisibility Rule for 6

If a number is divisible by both 2 and 3, then it is divisible by 6.

We already know that all even numbers are divisible by 2.

So, all even numbers which are divisible by 3 are divisible by 6.

## Divisibility Rule for 6 - Example

Problem :

Check whether 5832 is divisible by 6.

Solution :

The given number 5832 ends with 2.

So, it is even number and divisible by 2.

Check whether the number 5832 is divisible by 3.

5 + 8 + 3 + 2  =  18

The sum of the digits in the given number 5832 is 18 which is a multiple of 3.

Therefore, the given number 5832 is divisible by both 2 and 3.

So, the given number 5832 is divisible by 6.

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## Divisibility Rule for 7

In a number, if the difference between twice the digit in one's place and the number formed by other digits is either zero or a multiple of 7, then the number is divisible by 7.

## Divisibility Rule for 7 - Example

Problem :

Check whether 504 is divisible by 7.

Solution :

Twice the digit in one's place is

=  2 ⋅ 4

=  8

The number formed by the digits except the digit in one's place is

=  50

The difference between twice the digit in one's place and the number formed by other digits is

=  50 - 8

=  42

42 is divisible by 7.

So, the given number 504 is divisible by 7.

## Divisibility Rule for 8

In a number, if the last three digits are zeros or the number formed by the last 3 digits is divisible by 8, then the number is divisible by 8.

## Divisibility Rule for 8 - Example

Problem :

Check whether 789516 is divisible by 8.

Solution :

In the given number 789516, the last three digits are not zeroes.

But, the number formed by the last three digits is 516 which is divisible by 8.

So, the given number 789516 is divisible by 8.

## Divisibility Rule for 9

If the sum of the digits of a number is divisible by 9 or multiple of 9, then it is divisible by 9.

## Divisibility Rule for 9 - Example

Problem :

Check whether 12708 is divisible by 9.

Solution :

Add all the digits in the number 12708.

1 + 2 + 7 + 0 + 8  =  18

The sum of the digits in the given number 12708 is 18 which is a multiple of 9.

So, 12708 is divisible by 9.

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## Divisibility rule of 10

If a number ends with 0, then it is divisible by 10.

Examples :

10, 40, 300, 500, 450

## Divisibility Rule for 10

Problem :

Check whether 9470 is divisible by 10.

Solution :

The number 9470 ends with 0.

So, it is divisible by 10.

Need more examples If you would like to have practice problems on divisibility rules,

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You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 