Ginti Vedic

Vedic Division Calculator

Type a dividend and a divisor and watch Nikhilam, Paravartya or the Dhvajanka flag method find the quotient and remainder, next to long division.

Dividend

Divisor

Try a classic example

1,234 ÷ 89

Remainder 77. Solved with Nikhilam Navatashcaramam Dashatah

Sutra used

Nikhilam Navatashcaramam Dashatah

निखिलं नवतश्चरमं दशतः

“All from 9 and the last from 10”

89 is just 11 below 100, so the division needs only its small complement: no trial quotients and no long subtractions.

Watch it worked out: Nikhilam Navatashcaramam Dashatah

Step 7 of 7

So 1,234 ÷ 89 = 13 remainder 77. Check: 13 × 89 + 77 = 1,234.

What you entered

Dividend: 1,234Divisor: 89

1
Pick the base and write the complement (all from 9, the last from 10)
100 − 89= 1, 1
2
Split the dividend: the last 2 digits form the remainder part
12 | 34= 2 quotient digits, 2 remainder digits
3
Column 1: its total is the next quotient digit; multiply it by 1, 1
1 = 1, 1 × (1, 1)= write 1, 1 under the next 2 columns
4
Column 2: its total is the next quotient digit; multiply it by 1, 1
2 + 1 = 3, 3 × (1, 1)= write 3, 3 under the next 2 columns
5
Add up each remainder column
(3 + 1 + 3) | (4 + 3)= 7 | 7 → 77
6
Read the quotient part, carrying any total of 10 or more to the left
1 | 3= 13
7
Answer, checked by multiplying back
13 × 89 + 77 = 1,234= 13 remainder 77

Result

Quotient and remainder: 13 remainder 77

89 is just 11 below 100, so the division needs only its small complement: no trial quotients and no long subtractions.

What you entered

Dividend: 1,234Divisor: 89

1
Digit sums of the quotient 13, the divisor 89 and the remainder 77
1 + 3 = 4; 8 + 9 = 17 → 1 + 7 = 8; 7 + 7 = 14 → 1 + 4 = 5= 4, 8, 5
2
Multiply the first two, add the third and reduce
4 × 8 + 5 = 37= 1
3
Digit sum of the dividend 1,234
1 + 2 + 3 + 4 = 10 → 1 + 0 = 1= 1
4
Compare the two
1 and 1= match: the answer checks out

Result

Check: Passes

Quotient × divisor + remainder gives back the dividend, so their digit sums must agree too. A match doesn't prove the answer, but a mismatch always means a slip.

What you entered

Dividend: 1,234Divisor: 89

1
Bring down 3: 89 goes into 123 once, so the next quotient digit is 1
123 − 1 × 89= 34 left over
2
Bring down 4: 89 goes into 344 3 times, so the next quotient digit is 3
344 − 3 × 89= 77 left over
3
Read the quotient digits
1 | 3= 13 remainder 77

Result

Quotient and remainder: 13 remainder 77

Both give 13 remainder 77. Long division guesses a quotient digit at every step and subtracts; the Vedic method only multiplies by the small complement and adds.

Vedic working for the divisions people practise most

Each row is the last line of the Vedic working this calculator shows, with the sutra it picks. The bar separates the quotient part from the remainder part, read after adding down the columns; where a second pair follows, the remainder part was out of range and has been brought back.

Division	Sutra	Working	Answer
1011 / 9	Nikhilam (base 10)	112 \| 3	112 r 3
2134 / 9	Nikhilam (base 10)	236 \| 10 = 237 \| 1	237 r 1
1234 / 89	Nikhilam (base 100)	13 \| 77	13 r 77
9999 / 89	Nikhilam, remainder too big	108 \| 387 = 112 \| 31	112 r 31
10101 / 88	Nikhilam (base 100)	114 \| 69	114 r 69
23456 / 997	Nikhilam (base 1000)	23 \| 525	23 r 525
1234 / 11	Paravartya (base 10)	112 \| 2	112 r 2
1313 / 12	Paravartya (base 10)	109 \| 5	109 r 5
13456 / 112	Paravartya (base 100)	120 \| 16	120 r 16
1200 / 112	Paravartya, negative remainder	11 \| -32 = 10 \| 80	10 r 80

The remainder part always has as many digits as the base has zeros, so dividing by 89 (base 100) leaves two and dividing by 997 (base 1000) leaves three. Because the columns are added without carrying, the remainder part can come out too big, as in 9999 / 89, or negative with Paravartya, as in 1200 / 112; taking out or borrowing whole divisors fixes it. Every answer is also confirmed by long division.

Nikhilam division: 1234 ÷ 89 with no trial quotients

89 is 11 below 100, so write its complement 1, 1 and split 1234 into 12 | 34, keeping one remainder digit for each zero in 100. Bring down 1 as the first quotient figure and write 1 × (1, 1) = 1, 1 under the next two columns. The second column is now 2 + 1 = 3, so write 3, 3 under the two columns after it. Add down the remainder columns: 3 + 1 + 3 = 7 and 4 + 3 = 7. The quotient is 13 and the remainder 77, and 13 × 89 + 77 = 1234. There is no guessing how many times 89 goes in, only small multiplications by the complement.

Paravartya Yojayet: divide by 12 or 112 by flipping the surplus

"Transpose and apply" handles divisors just above a power of 10. 112 is 12 above 100, so write the surplus with its signs flipped: −1, −2. For 13456 ÷ 112, split 134 | 56. Bring down 1 and write −1, −2 under the next two columns, so the second column is 3 − 1 = 2; its −2, −4 make the third column 4 − 2 − 2 = 0. The remainder columns add up to 5 − 4 = 1 and 6, so the quotient is 120 and the remainder 16. When the remainder part comes out negative, borrow one divisor from the quotient to fix it.

Frequently asked questions

Which divisors suit Vedic division?

Nikhilam suits a divisor just below a power of 10 whose complement is made of small digits: 8, 9, 88, 89, 98, 997 or 9,989. Paravartya suits a divisor just above one: 11, 12, 13, 112, 1,012 or 1,103. For any other divisor, such as 47, it uses Dhvajanka, the flag method, which works for every divisor.

How does Dhvajanka division work?

Split the divisor into its first digit and a flag made of the rest: 47 becomes 4 with flag 7. Each column puts the remainder in front of the next digit, takes away the flag times the quotient digit before, and divides by 4. For 5735 ÷ 47: 5 ÷ 4 = 1 r 1; 17 − 7 = 10, 10 ÷ 4 = 2 r 2; 23 − 14 = 9, 9 ÷ 4 = 2 r 1; and the remainder column gives 15 − 14 = 1. So 5735 ÷ 47 = 122 remainder 1.

Why does the remainder sometimes come out bigger than the divisor?

The columns are added without carrying, so the remainder part can come out at or above the divisor. In 9999 ÷ 89 it reads 387. Take out as many divisors as fit (387 = 4 × 89 + 31) and add that number to the quotient: 108 + 4 = 112, remainder 31. With Paravartya the remainder part can come out negative instead; then borrow divisors from the quotient.

How do I check a division with digit sums (Beejank)?

Reduce the quotient, the divisor and the remainder to single digits by adding their digits. Multiply the first two, add the third and reduce again: it must match the digit sum of the dividend. For 1234 ÷ 89 = 13 remainder 77: 4 × 8 + 5 = 37, which reduces to 1, and 1 + 2 + 3 + 4 = 10, which also reduces to 1.

Do the sutras really come from the Vedas?

Jagadguru Swami Bharati Krishna Tirthaji attributed them to an appendix of the Atharvaveda in his 1965 book Vedic Mathematics, but they have not been found in any known Vedic text, and historians of mathematics regard them as his own modern formulations. The methods are correct arithmetic either way, and every answer here is checked against long division.