Home » Vedic Maths Tricks » Division in Vedic Mathematics

There are so many shortcuts for multiplication but hardly any shortcuts for division. Nandeesh has translated a Sanskrit Sutra to reduce long division to one line short-cut. Join me in thanking him for his great efforts.

Long Division reduced to one-line shortcut

Example 1:  716769 ÷ 54.

Reduce the divisor 54 to 5 pushing the remaining digit 4 “on top of the flag” (Dhvajanka so to say).

Corresponding to the number of digits flagged on top (in this case, one), the rightmost part of the number to be divided is split to mark the placeholder of the decimal point or the remainder portion.

Let us walk through the steps of this example:
716769 ÷ 54 = 13273.5


  1. 7 ÷ 5 = 1 remainder 2. Put the quotient 1, the first digit of the solution, in the first box of the bottom row and carry over the remainder 2
  2. The product of the flagged number (4) and the previous quotient (1) must be subtracted from the next number (21) before the division can proceed. 21 – 4 x 1 = 1717 ÷ 5 = 3 remainder 2. Put down the 3 and carry over the 2
  3. Again subtract the product of the flagged number (4) and the previous quotient (3), 26 – 4 x 3 = 1414 ÷ 5 = 2 remainder 4. Put down the 2 and carry over the 4
  4. 47 – 4 x 2 = 3939 ÷ 5 = 7 remainder 4. Put down the 7 and carry over the 4
  5. 46 – 4 x 7 = 1818 ÷ 5 = 3 remainder 3. Put down the 3 and carry over the 3
  6. 39 – 4 x 3 = 27. Since the decimal point is reached here, 27 is the raw remainder. If decimal places are required, the division can proceed as before, filling the original number with zeros after the decimal point27 ÷ 5 = 5 remainder 2. Put down the 5 (after the decimal point) and carry over the 2
  7. 20 – 4 x 5 = 0. There is nothing left to divide, so this cleanly completes the division

Example 2:  45026 ÷ 47

Reduce the divisor 47 to 4 pushing the remaining digit 7 “on top of the flag” (Dhvajanka so to say).

Corresponding to the number of digits flagged on top (in this case, one), the rightmost part of the number to be divided is split to mark the placeholder of the decimal point or the remainder portion.

Let us walk through the steps of this example:

45026 ÷ 47 = 958.0

4 9 7 5
47 4 5 0 2 6
0 9 5 8 0
  1. 4 ÷ 4 = 0 remainder 4. Put the quotient 0, the first digit of the solution, in the first box of the bottom row and carry over the remainder 4
  2. The product of the flagged number (7) and the previous quotient (0) must be subtracted from the next number (45) before the division can proceed. 45 – 7 x 0 = 4545 ÷ 4 = 9 remainder 9. Put down the quotient 9 and carry over the remainder 9.
  3. Again subtract the product of the flagged number (7) and the previous quotient (9), 90 – 7 x 9 = 2727 ÷ 4 = 5 remainder 7. Put down the quotient 5 and carry over the remainder 7.
  4. 72 – 7 x 5 = 3737 ÷ 4 = 8 remainder 5. Put down the quotient 8 and carry over the remainder 5.
  5. 56 – 7 x 8 = 0there is nothing left to divide, so this cleanly completes the division.

In reply to the query of Pratiush

To divide 716769 by 156:  Split divisor as 15 and 6

———————     11        17       12             12      15        9

15 6               71         6          7         6               9        0        0

—————– 4         5          9         4               6        7        3

Answer:  4594.673

Remarks:  In the first step we have written that 4 ÷ 4 = 0 remainder 4 instead of 4 ÷ 4 = 1 remainder 0. Otherwise, in the following step, we would have to subtract 7*1=7 from 05 which is not possible.

This post is contributed by Nandeesh Nagarajaia. He is a Chemical Engineer who did his B.Tech from NIT Suratkal.  He is now in IT field as Assistant General Manager(Systems) in Hindustan Copper Limited.

Other guest posts by Nandeesh –

  1. Quick Method to evaluate polynomials – Horner’s Method
  2. Quick calculations for extremely large numbers
  3. Shortcut multiplication for approximate numbers
  4. Heron’s method of finding roots

About

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

comments

  1. Norine says:

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  2. El says:

    I have a few questions as there are many variations in dhvajanka sutra. 1- what is the criteria for placing decimal? 2- in 745623/79=9438.26 why the first two digits are divided by 7 even though the first digit (7) is not less than 7. Same is the case with 7453/79. While 500001/89 is understandable, sois
    4- in 7632/94, why remainder 18 is left out when 18 is divisible by 9?

  3. El says:

    Ex 2, 45026/47, step 3.
    27/4= 5 remainder 7. Why not 27/4= 6 remainder 3??

  4. naga says:

    Can we apply this trick to every division or are there any particular set of rules to satisfy to apply this method. plz infrom me asap :)

  5. Bhupesh Aurangabadkar says:

    Kindly solve and explain the result for following..

    92356/54

  6. Bhupesh Aurangabadkar says:

    Hello,
    Kindly explain the procedure to solve 55026 / 57 and 54026/57 ???

    Thanks lot in advance.

    Bhupesh

  7. Sameer Dubey says:

    Now its great …please EDIT as requested and dont mess up this nice method..great job!!

  8. Sameer Dubey says:

    u could explicitly say we have to take one lower quotient than what it is … in second case.sorry for being harsh

  9. Sameer Dubey says:

    please stop cheating in name of IIT,what bullshit is this,u are getting answer by hook.which iit gave u admission when u do “27 ÷ 4 = 5 remainder 7″.

    • admin says:

      Dear Mr.Sameer,

      I would suggest you to be respectful of selfless people like Nandeesh who’ve contributed this post. BTW he is from NIT and not IIT.

      What ever he has written is factually correct. So please read it carefully to understand the crux of the trick.

      Thanks

      • Man-E-faces says:

        Dear Vineet,

        Read this comment from Sameer. I feel pity on him. Don’t waste you time explaining goodness to such people. They are leeches that suck your productive time. Simply delete his comment and let him go into oblivion.

        Regards.

  10. Rakesh Rajbhar says:

    Dear Nandeesh Sir,
    Pease solve 92356 divided by 59.

    Thanks

  11. Aakarsh says:

    I was unable to get the right answer for 6489/56 with this method. something weird happens at the end…

  12. kokok says:

    im confused about 4 divided by 4 is 0? it is 1 right? how could it be 0?

  13. supriya says:

    hi vineet,

    need to know the steps involved in the division of 716769/156…could you please explain

  14. kumar says:

    Hi Nandeesh thanks a lot for the above tip. could you please clearly explain division of 716769 by 156. i missing something when the flag number greater than 5. Please help me

  15. ratnesh says:

    sir, i am having problem in long division tricks, like it is ok , till u get 3 digit number as a divisor and especially like up to 30?s(EX.154, 298,267,), but if d divisor cmes as 435, 414, then wt to do and hw to do,…..and if divisor is of 4 or 5digit long, den wt to do!!!!???pls give me solution sir, as soon as possible

  16. vinay says:

    Can you help me in division of 2187 by 36 please solve

  17. Karan says:

    how will we divide 2156 by 31 ,using above method????

    • Karan says:

      i cant understood how remainder can be greater than diviser?? in yours 2nd example

    • vinod kumar says:

      3 2

      3 1 2 1 5 6

      6 9 17

      Step 1 Divide 21 by 3= 7 rem 0 So we can divide as 21/3=6 rem 3
      Step 2 Next digit becomes 35 i.e 35-(6*1)=29,and 29/3=9 rem 2
      Step 3 Next digit is 26 and 26-(9*1)= 17
      So the answer is 69 rem 17

  18. I luv vedic math says:

    Superb trick! There were other Vedic math tricks that I found but this one is awesome. Very simple to understand and execute. Thanks to Nandeesh for finding and translating the Sanskrit Sutra.

    Thanks again!!
    Naren

  19. Nuuky says:

    I solved the division 716769 ÷ 156 dividing first both numbers by 3 ( and at the end the answer will be the same, because they are multiples of 3 )

    1) 716769 ÷ 3= 238923

    156 ÷ 3 = 52

    2) So we have now:

    238923 ÷ 54 =

    Now, it is easier to solve it like the first example in this page.

    We reduce the divisor 52 to 5 pushing the remaining digit 2 “on top of the flag”

    2 3 5 4 4 5 3 1
    5 23 8 9 2 3 0 0 0
    4 5 9 4 . 6 7 3

    • Nuuky says:

      The numbers appeared moved after I submitted it, so I would like to clarify the order in the last row of numbers, which is the answer.

      The number 4 should be under the 23, the 5 under the 8, the 9 under the 9, the 4 under the 2 and then the decimal or remainder 6 under the 3, the 7 under the first 0 and the 3 under the second 0 at the right.

      2 3 5 4 4 5 3 1
      5 23 8 9 2 3 0 0 0
      4 5 9 4 . 6 7 3

  20. Ayushman says:

    Superb method for division. I tried finding a suitable method for division in many books. This one is the simplest and most useful one I have ever crossed across. Thanks a lot………!!

  21. kashir says:

    please explain when flag number is more than 5.i dont know what i am missing.
    for eg:14575 is divided by 59 or 58

  22. Musthaq says:

    Can u pls tell me how to divide trickly with 3 digits of divisor with first method(metho with columns)??????

  23. prabhu says:

    sir i need a vedic divider circuit (digital or cmos circuit at least for 4 or 8 bits)could you help me

  24. Joydeep Sarkar says:

    Can you please explain me the steps to divide 76 by 75?I don’t know what error i am committing.Please help.

  25. shekhar rajak says:

    ur r always give awsme tricks …

  26. Tanveer says:

    Awesome Man!!

    Gud trick..i loved it;-)

  27. Rishi says:

    STEP 3 : 27/4 = 6 Quotient and 3
    step 5: similar mistake
    plz solve this sir i m also confuse

  28. [...] Long Division reduced to one-line shortcut [...]

  29. ritu says:

    plz explain me the method when divisior is of 4 digit.

  30. Rajesh says:

    its not more tricky. i need easy calculations for my bank exams

  31. abhi says:

    pls suggest any other method. this is more complicated than the actual division.

  32. raghvendra says:

    can somebody apply same rule in dividing 45693 by 68

  33. gaurav anand says:

    pls solve follow equation wid explanation
    79589/59

  34. gaurav anand says:

    is d trick apply on following calculation
    79589/59

  35. chitra bisht says:

    plsome give some easy tricks of division

  36. pranav aggaarwal says:

    very very gud

    its new for me

  37. NANDEESH H N says:

    TO DIVIDE 4321 BY 1234

    63 4 20 77 28 10
    123 4 432 1 0 0 0 0 0
    3 5 0 1 6 2 0

    ANSWER 3.50162

    • Navin says:

      Hi Nanadeesh, In example# 716769 ÷ 54 = 13273.5. how did u come to know the that the decimal point will come at last digit only, y not last two. Because u have left only last box in example. Im asking this because decimal before two or three digit than what we can do?

  38. Abhay says:

    Can you please give a detailed explaantion of a 4 digit number divided by a four digit number? e.g. 4321/1234

  39. NANDEESH H N says:

    TO DIVIDE 716769 BY 156: SPLIT DIVISOR AS 15 AND 6

    11 17 12 12 15 9
    15 6 71 6 7 6 9 0 0
    4 5 9 4 6 7 3

    ANSWER: 4594.673

  40. Pratiush says:

    Nice short cut.could u give an exmaple where lets say, 716769 is divided by 156.

    • NANDEESH H N says:

      HERE THE DIVISOR IS SPLIT AS 15 AND 6.

      11 17 12 12 15 9

      15 6 71 6 7 6 9 0 0

      4 5 9 4 6 7 3

      ANSWER 716769 / 156 = 4594.673

      HINT: TRY TO REDUCE THE DIVISOR TO FACTORS AND DIVIDE BY FACTORS ONE BY ONE.

    • NANDEESH H N says:

      716769 / 15 —> HERE SPLIT DIVISOR AS 15 AND 6

      11 17 12 12 15 9
      15 6 71 6 7 6 9 0 0
      4 5 9 4 6 7 3

      ANSWER: 716779 / 156 = 4594.673

  41. NANDEESH H N says:

    I have only transmitted what I have gathered from somewhere else. Pl. give me credit only for spreading it.

    • Manoj says:

      STEP 3 : 27/4 = 6 Quotient and 3
      step 5: similar mistake

      • NANDEESH H N says:

        See the remarks.

        Remarks: In the first step we have written that 4 ÷ 4 = 0 remainder 4 instead of 4 ÷ 4 = 1 remainder 0. Otherwise, in the following step, we would have to subtract 7*1=7 from 05 which is not possible.

        Similar logic applies everywhere.

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I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths

I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more

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