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
- 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
- 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
- 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
- 47 – 4 x 2 = 3939 ÷ 5 = 7 remainder 4. Put down the 7 and carry over the 4
- 46 – 4 x 7 = 1818 ÷ 5 = 3 remainder 3. Put down the 3 and carry over the 3
- 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
- 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 | |||
4^{7} | 4 | 5 | 0 | 2 | 6 | |
^{0} | ^{9} | ^{5} | ^{8} | ^{ } | ^{0} |
- 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
- 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.
- 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.
- 72 – 7 x 5 = 3737 ÷ 4 = 8 remainder 5. Put down the quotient 8 and carry over the remainder 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 –
- Quick Method to evaluate polynomials – Horner’s Method
- Quick calculations for extremely large numbers
- Shortcut multiplication for approximate numbers
- Heron’s method of finding roots
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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?
Ex 2, 45026/47, step 3.
27/4= 5 remainder 7. Why not 27/4= 6 remainder 3??
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
because i am not able to solve the following problem using the same trick please clarify:
71804/29
Kindly solve and explain the result for following..
92356/54
Hello,
Kindly explain the procedure to solve 55026 / 57 and 54026/57 ???
Thanks lot in advance.
Bhupesh
Now its great …please EDIT as requested and dont mess up this nice method..great job!!
u could explicitly say we have to take one lower quotient than what it is … in second case.sorry for being harsh
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″.
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
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.
Dear Nandeesh Sir,
Pease solve 92356 divided by 59.
Thanks
I was unable to get the right answer for 6489/56 with this method. something weird happens at the end…
im confused about 4 divided by 4 is 0? it is 1 right? how could it be 0?
hi vineet,
need to know the steps involved in the division of 716769/156…could you please explain
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
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
Can you help me in division of 2187 by 36 please solve
also please help how r u deciding the position of the decimal point
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
Pl correct 31 in place of 32 in the first line
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
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
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………!!
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
Can u pls tell me how to divide trickly with 3 digits of divisor with first method(metho with columns)??????
sir i need a vedic divider circuit (digital or cmos circuit at least for 4 or 8 bits)could you help me
Can you please explain me the steps to divide 76 by 75?I don’t know what error i am committing.Please help.
ur r always give awsme tricks …
Awesome Man!!
Gud trick..i loved it;-)
STEP 3 : 27/4 = 6 Quotient and 3
step 5: similar mistake
plz solve this sir i m also confuse
[...] Long Division reduced to one-line shortcut [...]
plz explain me the method when divisior is of 4 digit.
its not more tricky. i need easy calculations for my bank exams
pls suggest any other method. this is more complicated than the actual division.
can somebody apply same rule in dividing 45693 by 68
Bro. same rule can b applied on 45693 by 68..itz simple..try it..:-)
pls solve follow equation wid explanation
79589/59
is d trick apply on following calculation
79589/59
Yeahh!!
This trick cn be applied on ur query…try it..:-)
plsome give some easy tricks of division
very very gud
its new for me
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
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?
Can you please give a detailed explaantion of a 4 digit number divided by a four digit number? e.g. 4321/1234
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
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
nice post. thanks.
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.