Multiply numbers near 100 instantly (Nikhilam sutra)
100 के पास की संख्याओं का तुरंत गुणा (निखिलम् सूत्र)
The Vedic sutra “Nikhilam Navatashcaramam Dashatah” turns 97 × 96 or 103 × 107 into one subtraction and one small multiplication.
97 × 96 जैसे गुणा: दोनों का 100 से अंतर लें, क्रॉस में घटाएं/जोड़ें और अंतरों का गुणनफल अंत में लिखें।
Both numbers below 100
- Write how much each number is below 100 (97 → −3, 96 → −4).
- Left part: subtract crosswise — 97 − 4 (or 96 − 3) = 93.
- Right part: multiply the differences — 3 × 4 = 12, written with two digits.
- Join: 93 | 12 → 9312.
Example 97 × 96
−3 and −4 → 93 | 12 → 9312
Example 94 × 97
−6 and −3 → 91 | 18 → 9118
Example 88 × 95
−12 and −5 → 83 | 60 → 8360
Both numbers above 100
- Differences are positive.
- Left: add crosswise. Right: multiply the differences.
Example 103 × 107
+3 and +7 → 110 | 21 → 11021
Example 105 × 108
+5 and +8 → 113 | 40 → 11340
One above, one below
The product of the differences is negative, so borrow 1 from the left part (worth 100).
Example 98 × 103
−2 and +3 → left 98 + 3 = 101, right −6 → 101 | −6 = 10100 − 6 = 10094
Try it yourself · अभ्यास
- 99 × 99 = ?
Show answer
98 | 01 → 9801
- 96 × 98 = ?
Show answer
94 | 08 → 9408
- 102 × 109 = ?
Show answer
111 | 18 → 11118