Friday, September 25, 2015

Test of Divisibility of a number

Find divisibility by numbers

Hi Friends,

Lets learn about divisibility of a given number by another  numbers. These rules are really helpful while calculating other examples of Quantitative Aptitude or Numerical Ability Section of all the examinations. 

Group 1

Divisibility By 2:  

     A number is divisible by 2, When number’s unit digit (last digit) is divisible by 2. Means last digit should be one of 0,2,4,6,8.

     e.g. 14,28,522.

Divisibility By 4:  

     A number is divisible by 4,  When a number formed by last two digit is divisible by 4. 
     e.g. 1416, here number formed by last two digit is 16 which is divisible by 4. so the whole number 1416 is divisible by 4

Divisibility By 8:  

     A number is divisible by 8 When a number formed by last three digit is divisible by 8. 
e.g. 11328 here a number formed by last three digit is 328 which is divisible by 8. so the whole number 11328 is divisible by 8.

Group 2

Divisibility By 3:  

     A number is divisible by 3  When a sum of all digits is divisible by 3.
     e.g. 1362. here 1+3+6+2=12 and 12 is divisible by 3 so the number 1362 will be divisible by 3.

Divisibility By 9:  

     A number is divisible by 9 When a sum of all digits is divisible by 9.
     e.g. 7092. here 7+0+9+2=18 which is divisible by 9 so the number 7092 will be divisible by 9.

Group 3

Divisibility By 5:  

     A number is divisible by 5 When the unit digit is 0 or 5.

Divisibility By 10:

     A number is divisible by 10 When the unit digit is 0.

 Group 4

Divisibility By 7:

     To check divisibility by 7, Take the last digit in an number, double the last digit and subtract it from the remaining number. Now check if the result is divisible by 7. For larger(4 digit) numbers repeat the process.
Simply, “if the difference of double of last digit and remaining number is 0 or divisible by 7”

Lets take an example,
Ex-1: 686 , here last digit is 6, so double of last digit is 12. so subtracting 12 from the remaining number i.e. 68 - 12 = 56. here we can say easily 56 is divisible by 7 and so 686 will also be divisible by 7.

Ex-2: 3794, here last digit is 4, so double of last digit is 8. so subtracting 8 from the remaining number i.e.379 - 8 =371. here by first observation we can't say whether 371 is divisible by 7 or not. so lets repeat the process for 371. 
last digit is 1 , subtracting its double from remaining number 37-2=35. which is divisible by 7. so the given number 3794 is divisible by 7. 

Procedure for divisibility of another numbers in this group are similar with some differences. so i will only point out the differences here for the next three numbers. You should try the method and check divisibility of some numbers yourself.

Tip : Save the infographics to your computer or mobile. And revise on the go.

Divisibility By 13:

     To check divisibility by 13, take the last digit then if the sum of 4 times of last digit and remaining number is divisible by 13.

Divisibility By 17:

     To check divisibility by 17, take the last digit then if the difference of 5 times of last digit and remaining number is divisible by 17.

Divisibility By 19:

      To check divisibility by 19, take the last digit then if the sum of double of last digit and remaining number is divisible by 19.

To remember the divisibility rules of 7,13,17 & 19 properly see the orange coloured words in the picture above.

Divisibility by 11,14,15,24,40,36

Divisibility By 11:

To check divisibility by 11, take difference between the sum of number placed at even and odd places. If the difference is divisible by 11 or the difference is 0 then the number is divisible by 11.

 E.G. 49731,

here the odd placed number's sum: 1+7+4=12
even placed number's sum: 3+9=12

so difference between sum of even and odd place is 0. so 49731 is divisible by 11.

Divisibility By Composite Numbers (14,15,24...)

A number(X) is divisible by another composite number(Y) if X is divisible by both co-prime factors (p & q) of Y

e.g. given number is 3072.
Lets check divisibility by a composite number 12.
Here X = 3072 , Y = 12, and p=4, q=3. 
where 4 & 3 are two coprime factors of 12.

Now for divisibility by 3, 3+0+7+2=12. so 3072 is divisible by 3.
For 4, last two digits 72 is divisible by 4 , so 3072 is also divisible by 4.
so 3072 will also be divisible by 12.

Another Examples of Composite number divisibility are given in the above infographics.

Hope you find this article informative, if you have any suggestions then please share in the comments below.


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