Quicker Maths

## Division in Vedic Mathematics

Posted on October 4, 2010

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

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 -

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#### Posted by Vineet Patawari

1. 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

2. 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

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

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

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

• 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

5. 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

6. 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

• 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

7. 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………!!

8. 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

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

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

12. ur r always give awsme tricks …

13. Awesome Man!!

Gud trick..i loved it;-)

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

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

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

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

18. can somebody apply same rule in dividing 45693 by 68

19. pls solve follow equation wid explanation
79589/59

20. is d trick apply on following calculation
79589/59

21. plsome give some easy tricks of division

22. very very gud

its new for me

23. 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

• 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?

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

25. 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

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

• 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.

• 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

27. nice post. thanks.

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

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

• 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.