Most people learned a complicated and time consuming way to do long division, developed by mathematician Henry Briggs. The Briggs method uses an algorithm or shortcut for working through the mathematical proof of long division. It is an arduous method requiring practice to master. In contrast to the Briggs "western" method, mathematician Swami Sri Bharati Krishna Teerthaji wrote a long division algorithm based on Vedic text that is much easier to calculate.

Learn the vocabulary. The number 5 goes into 568 113 even times with 3 left over. This is written as 568 ÷ 5 = 113 remainder 3. The number 568 is called the dividend, 5 is called the divisor, 113 is the quotient and the 3 left over is called the remainder. It is important to understand this vocabulary so you can follow instructions on what to do with each part of the division equation. In Vedic mathematics all division is performed using an algorithm with a corrective factor based on the number 10. For division by nines, for example, the corrective factor is one because 10  9 =1. Similarly the corrective factor for division by 8 is 2, because 10  2 = 8, for 7 it is 3, 6=4 and so forth.

Start by learning the Vedic algorithm for division by nines. This is the easiest one because the corrective factor is one, meaning you multiply by one. Since one times any number is still just that number, eg. 91 = 9, 101=10 and 156*1=156, you can just pretend there is no correction factor. For the problem 32 ÷ 9 = 3 remainder 5, 32 is the dividend, 9 is the divisor, 3 is the quotient and 5 is the remainder.

Take the first digit of the dividend (3 in 32) and write that down as the first number in your answer. Division by nine always results in an answer that reproduces the first number in the dividend.
32 ÷ 9
= 3 as the first number of the answer. Always just copy the first digit of the dividend down putting it on the line underneath and lined up with the dividend.
Take the 3 and add it to the next number of the dividend.
32 ÷ 9
= 3 first digit
= 5 is your remainder (3+2) =5

Practice the Vedic method with progressively more complicated numbers. For the problem 321 ÷ 9 the method works the same.
321 ÷ 9
= 3 is the first digit
= 5 is the second digit (3+2)
= 6 is the remainder (5+1)
The quotient is 35 and the remainder is 6
For an even larger number such as 12311 ÷ 9
12311 ÷ 9
= 1 is the first digit
= 3 is the second digit (1+2)
= 6 is the third digit ((3+3)
= 7 is the third digit is 7 (6+1)
= 8 is the remainder (7+1)
The quotient is 1367 and the remainder is 8.

Use the corrective factor when dividing by numbers other than nine. For the problem 31 ÷ 8 = 3 R 7. After coping the first digit of the dividend (3 of 31), complete the same algorithm as before, only multiple each number by two.
31 ÷ 8
= 3 is the first digit
= 7 is the remainder (3*2) +1
The quotient is 3 and the remainder is 7.
For more complicated problems, the procedure is the same. The quotient of 310 ÷ 9 is 38 with a remainder of 6.
310 ÷ 8
= 3 is the first digit
= 7 is the second digit (3*2) +1
= 14 is the remainder (7*2) +0
Since the divisor 8 goes into 14 once with a remainder of 6 the final answer is
37 + 1, remainder 6
or 38 remainder 6.
Perform all other division for single digit divisors from 7 through 2 but multiplying by the appropriate corrective factor.
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