Vedic Maths — Veda Topper

Base Multiplication (Nikhilam) — Numbers Near 100

When two numbers sit close to a base like 100, you can multiply them almost instantly using the sutra Nikhilam Navatashcaramam Dashatah. Find how far each is from the base, cross-subtract, and multiply the little differences.

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97−396−497 − 4 = 933 × 4 = 12= 9312
Base multiplication 97 × 96: deficits are 3 and 4; cross-subtract for 93 and multiply the deficits for 12 → 9312.

The rule (numbers just below 100)

  1. Write how far each number is below 100 (its deficit).
  2. Left part = one number minus the other number's deficit (both ways give the same answer).
  3. Right part = the two deficits multiplied (write it as 2 digits).
Example 1 — 97 × 96
Deficits: 100−97 = 3, 100−96 = 4 Left: 97 − 4 = 93 (or 96 − 3 = 93) Right: 3 × 4 = 12 Join: 93 | 12
97 × 96 = 9312
Example 2 — 98 × 88
Deficits: 2 and 12 Left: 98 − 12 = 86 Right: 2 × 12 = 24 Join: 86 | 24
98 × 88 = 8624
Example 3 (carry) — 88 × 88
Deficits: 12 and 12 Left: 88 − 12 = 76 Right: 12 × 12 = 144 → keep 44, carry 1 Left becomes 76 + 1 = 77
88 × 88 = 7744

Above the base

For numbers just above 100, use surpluses instead, and add the cross figure.

Example 4 — 103 × 104
Surpluses: 3 and 4 Left: 103 + 4 = 107 Right: 3 × 4 = 12 Join: 107 | 12
103 × 104 = 10712

Why it works

Writing the numbers as (100−a) and (100−b), their product is 100(100−a−b) + ab. The bracket is the "cross-subtract" step, and ab is the product of the deficits.

Practice (answers below):
1) 96 × 93   2) 99 × 97   3) 94 × 92   4) 102 × 106   5) 89 × 99

Answers: 1) 8928 2) 9603 3) 8648 4) 10812 5) 8811

More Vedic Maths tricks

Frequently asked questions

What is Nikhilam multiplication in Vedic Maths?
Nikhilam ("all from 9 and the last from 10") multiplies numbers near a base like 100 by using how far each is from the base: cross-subtract for the left part and multiply the differences for the right part.
Can Nikhilam multiply numbers above 100?
Yes. Use the surplus (how far above the base) and add the cross figure instead of subtracting. 103 × 104 = 10712.
When is base multiplication most useful?
When both numbers are close to 10, 100 or 1000 — such as 97 × 96 or 108 × 106 — where it is far faster than long multiplication.
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