### Vedic Math - Dividing Three and Four Digit Numbers by any Two Digit Numbers Near Base

In last article, we discussed about division of numbers by any one digit number (near base). In this article, we shall discuss about division of three and four digit numbers by any two digit numbers (near base).

If we are dividing by 2 digit number than we need to have 2 places in the right column.

Dividing three digit numbers by any two digit numbers

To divide abc by mn, we apply the same rule as before:
1) Put a, b and c in the first row (as shown below)
2) List p x a in the second column of the second row. (p = base- mn)
a | b c
| p x a
----------------
a |(p x a) + bc

Quotient: a, Remainder: (p x a) + bc

Example:
To divide 102 by 75, the nearest base is 100, so p = 100-75 = 25

102 divided by 75
1 | 02
| 25
--------------
1 | 27
Quotient= 1, Remainder= 27

234 divided by 73
p = 100 - 73 = 27
2 | 34
| 54
-------------
2 | 88    (Remainder(88) is greater than 73, Add 1 to quotient i.e. 2+1=3 and subtract divisor(73)                        from remainder i.e.(88-73=15))
3 | 15
New Quotient = 3, New remainder = 15

Dividing four digit numbers by any two digit numbers

abcd divided by mn

This gets a little more complicated and one must be very careful with the places in the columns.
p = base - mn = 100 - mn