DIVISIBILITY RULES

About "Divisibility rules"

Divisibility rules:

Here we are going to see the shortcuts to predict one number is divisible by another number with out doing too much calculation.

Once we remember these rules we can easily divide two numbers without calculator.

Learning this topic is more important for all the students who are in school to do visions in a easy way. Divisibility Test

Divisibility rules for 2

All even numbers are divisible by 2.

The number which ends with one of the following numbers, that is 0, 2, 4, 6 or 8 is known as even numbers. 

If the given ends with any of the above numbers, we can say that the given number is divisible by 2.

Divisibility test by 2 - Example

Example 1 :

Check whether 16 is divisible by 2 ?

Solution :

Let us test the number 16 is divisible by 2 or not. To test that divide 16 by 2. The result will be 8 (quotient) or the remainder is zero.

Hence, the given number "16" is exactly divisible by 2 

Need more examples

Divisibility rules for 3

To check whether the given number is divisible by 3 or not, we have to add the sum of the digits.

If the sum of the digits is divisible by 3, we can say that it is divisible by 3.

Divisibility test by 3 - Example

Example 2 :

Test whether 252 is divisible by 3?

Solution :

To check whether it is divisible by 3 or not we have to calculate the sum of the digits.

252 = 2 + 5 + 2 

= 9 ÷ 3 

= 3

Need more examples

Divisibility rules for 4

If the last two digits of the given number are zeroes or the last 2 digits are divisible by 4, we can say the given number is divisible by 4.

Divisibility test by 4 - Examples

Example 3 : 

Test whether 328 is divisible by 4?

Solution :

Since the last two digits are not zeroes, we have to check whether the last two digits are divisible 4. 

The last two two digits of the given number 328 is 28.Let us check whether it is divisible by 4 or not.

Need more examples

Divisibility rules for 5

All the numbers ending in 0 or 5 are divisible by 5 

Divisibility test by 5 - Examples

Example 4 :

Test whether 105 is divisible by 5 ?

Solution :

In the given number 185, the last digit 5.

Hence, the given number 105 is divisible by 5.

Need more examples

Divisibility rule of 6

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

Hence all even numbers which are divisible by 3 are divisible by 6

Example of divisibility by 6

Example 5 :

Test whether 5832 is divisible by 6?

Solution :

Here the given number is an even number. Hence it is divisible by 2. Now we have to check whether it is divisible by 3 or not for that we have to find the sum of the digits 5 + 8 + 3 + 2 = 18 . 


The sum of the digits is divisible by 3. Hence the given number 5832 is divisible by 3.

Need more examples

Divisibility rule of 9

A number is divisible by 9 if the sum of the digits is divisible by 9.

Example of divisibility by 9

Example 6 :

Test whether 998 is divisible by 8 ?

Solution :

Here sum of the digits of the given number 9 + 9 + 8 is "26" which is not divisible by 9 .

Hence, the given number 998 is divisible by 9.

Need more examples

Divisibility rule of 10

All numbers which end in 0,that is have 0 in the "ones" place are divisible by 10.

Ex:100,500,450..... are divisible by 10.

Example of divisibility by 10

Example 7 :

Test whether 9470 is divisible by 10 ?

Solution :

Here the last digit of the given number is 0.

Hence, the given number 9470 is divisible by 10.

Need more examples

Divisibility rule of 11

If the difference between the sum of one set of alternate digits and the sum of the other set of alternate digits is 0 or 11 or 22.....the numbers are divisible by 11. 

Example of divisibility by 11

Example 8 :

Test whether 198 is divisible by 11?

Solution :

In this three digit number the sum of the first and last number = middle number that is 1 + 8 = 9 So the whole number 198 is divisible by 11.

Need more examples

Divisibility rule of 12

All the numbers which are divisible by 3 and divisible by 4 are divisible by 12.

Example of divisibility by 12

Example 9 :

Check 8520 is divisible by 12 or not.

Solution :

Here the given number is 8520.According to the procedure first we have to check if the given number is divisible by 3.

For that we have to calculate the sum of the digits that is  8 + 5 + 2 + 0 = 15

So it is divisible by 3.

To check whether 8520 is divisible by 4 we need to consider the last two digits that is 20 

So it is divisible by 4.

Hence, the given number 8520 is divisible by 12.

Need more examples

Divisibility rule of 15

All the numbers which are divisible by 3 and divisible by 5 are divisible by 15.

Example of divisibility by 15

Example 10 :

Check whether the number 41295 is divisible by 15?

Solution :

Here we need to check the given number 41295 is divisible by 15 or not.

To check whether the given number is divisible y 15 or not first we have to check whether it is divisible by 3 and it is divisible by 5.

If the given number is divisible by both 3 and 5 we can say the given number is divisible by 15.So, first let us check 41295 is divisible by 3 for that we have to calculate the sum of the digits of the given number.

That is  4 + 1 + 2 + 9 + 5 = 21 

If we divide the sum of digits 21 by 3 we are getting 0 as the remainder. So we can decide it is divisible by 3.To check whether it is divisible by 5 we need to consider the last digit, that is 5. So it is divisible by 5.

Hence the given number is divisible by 15.

Need more examples

Divisibility rule of 18

All the numbers which are divisible by 2 and divisible by 9 are divisible by 18.

Example of divisibility by 18

Example 11 : 

Check whether 1458 is divisible by 18.

Solution :

If the given number is divisible by both 2 and 9.Then we can say it is divisible by 18.

Since the given number ends with 8, it is even number. 

All even numbers are divisible by 2.

Now we need to check if it is divisible by 9. To check whether it is divisible by 9 need to calculate the sum of the digits that is,

 1 + 4 + 5 + 8 = 18 

18 is divisible by 9

Hence, the given number 1458 is divisible by 18.

Need more examples

Divisibility rule of 25

If the last two digits of a numbers are 00, 25, 50 or 75 is divisible by 25. 

Example of divisibility by 25

Example 12 :

Check 3500 is divisible by 25.

Solution :

  • To check whether the given number is divisible by 25, we have to see the last two digits. 
  • If the last two digits are either 00 or 25 or 50 or 75 then the given number is divisible by 25.
  • The given number is 3500.
  • The last two digit is 00.
  • So the given number 3500  is divisible by 25.

Need more examples

Divisibility test - Related topics

Test on divisibility by 3

Test on divisibility by 4

Test on divisibility by 5

Test on divisibility by 6

Test on divisibility by 8

Test on divisibility by 9

Test on divisibility by 10

Test on divisibility by 11

Test on divisibility by 12

Test on divisibility by 15

Test on divisibility by 18

After having gone through the stuff given above, we hope that the students would have understood "Divisibility rules"

Apart from the stuff given above, if you want to know more about "Divisibility rules", please click here.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic 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


             Math dictionary