Maths Shortcuts





            Test of Divisibility
Divisibility by 2:- If the one’s place of whole number is even then                                   The whole number divided by 2.
                             E.g.  find 42 is divided by 2 or not.
Sol:- one’s digit is 2 which is even so 42 is divided By 2.
Divisibility by 3:- Add all numbers and divided by 3 if obtained sum
                              Is divided by 3 then the whole number is divided
                              By 3.
                              E.G.  find 27 is divisible by 3 or not.
Sol: - Add Numbers. 2+7=9 which is divisible by 3 so whole number         is  divided by 3.
Divisibility by 4:-Write one’s place & ten’s place if these two digits
                            Divided by 4 then whole number divided by 4.
                            E.G.  6464 is divide by  4 or not.
Sol:-  write one’s and ten’s place digit.
           64 which is divisible by 4 so whole number is divided by 4.
Divisibility by 5:- If one’s place is 5 or 0 then whole number divide
                               by 5.
                             E.g. 23567890 is divisible by 5 or not.
                             One’s digit is 0, so whole number is divided by 5.
Divisibility by 6:- Those Number who Divide by 2 and 3 is also
                               Divided by 6.
                             E.G.   216 is divisible by 6 or not.
Sol:- 216 is divisible by 2 and 3 so it is also divided by 6.
Divisibility by 7:- Multiply the one’s digit by 2.
                               Subtract this value from rest of number.
                               Continue this process until you know it is                                            divisible By 7.
E.G. 483 is divisible by 7 or not.
Sol:- According to method:- 3 X 2=6
         Subtract 48-6=42 which is divided by 7. So whole number is               divided by 7.
Divisibility by 8:- write one’s, tens and hundred digits of Number. If                                                             
                                These three digits divided by 8 then the whole
                                Number divided by 8.
                                E.G. 456986512 is divisible by 8 or not.
    Sol: - According to method:-  divide last three digits by 8 so 512 is
             Divided by 8 so whole number is divided by 8.
Divisibility by 9:- Add all numbers if the sum is divided by 9 then the
                              Whole number is divided by 9.
                              E.G. 81 is divisible by 9 or not.
        Sol:- Add the Numbers. 8+1=9 this is divisible by 9
                 So whole number is divided by 9.
Divisibility by 10:- If one’s place is 0 then the Whole number is
                                  Divided by 10.
E.G. 100
Sol:- one’s digit is 0, so whole number is divided by 10.
Divisibility by 11:- Write the numbers. To find its divisibility test we                                 
                                  Need to find difference between two sums.
                              E.g. To find 121 is divisible by 11 or not.
 
Number
Sum of Digits in odd places
Sum of digits in even places
Difference
Divisibility or not
121
1+1
2



2
2
0
yes

If difference is 0 or multiple of 11 then whole Number is divided by 11.
Divisibility By 12:- If the number is divided by 3 and 4 then consider
                                 Number is divided by 12.
                               E.G. 1728 is divided by 12 or not.
Sol: - 1728 is divided by 3 and 4 easily so whole number is divided
          By 12.

         





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