# 30MSC 2023 #15 :Nikhilam Division

Nikhilam or base division is a Vedic Math technique for quickly performing division when the divisor is a little smaller than a power of 10. Instead of actually using the divisor with its big digits, its ten’s complement is used as a multiplier. This 10’s complement is easily obtained using the Nikhilam Sutra, All From 9 and the Last from 10.

We will use the question given in the  Intermediate International Vedic Mathematics Olympiad to explain how the Nikhilam division is done: Using Nikhilam division for 24219 ÷ 897, some workings are shown below. What are the three missing digits for A, B and C?

1. Since the base of the divisor, 897, is 1000 which has 3 zeroes, the first step is to separate the last three digits of the dividend by a remainder bar. This will also be the location of the decimal point if we decide to decimalize the remainder.

8 9 7      |    2 4 | 2 1 9

• Next we will place the ten’s complement of the divisor below it and bring down the first digit of the dividend as the first digit of the quotient.

8 9 7      |    2 4|2 1 9

1 0 3      |

|___________

2

• Multiply 2 by the ten’s complement and place the product below the dividend starting at the second column: 2 x  103 = 206

8 9 7      |    2 4|2 1 9

1 0 3      |        2  0 6

|___________

2

• Add the figure of the second column to get the 2nd figure of the quotient. 4 + 2 = 6

8 9 7      |    2 4|2 1 9

1 0 3      |        2  0 6

|___________

2  6

• Multiply 6 by the 10’s complement of the divisor and place it starting at the 3rd column. Then add the figure in the remainder columns.

8 9 7      |    2 4|2 1 9

1 0 3      |        2  0 6

|            6 1 8

|_______________

2  6 | 8 9 7 = 2 7 |0 0 0

Since the remainder is equal to the divisor, we can add 1 to the quotient.

ABC then represents the digits 206

Other examples of base division are discussed in Chapter 5 of our forthcoming book 30 Master Strategies in Computing, Vol II.

Follow us on our Facebook page, MATH-Inic Philippines at https://www.facebook.com/MATHInicPhils to see tomorrow’s 30MSC 2023 #16: Transpose and Apply