Parāvartya Yojayet — Transpose and apply

परावर्त्य योजयेत् — Paraavartya Yojayet

Transpose and apply. Division by a near-10 divisor: transpose the sub-digits of the divisor (negate them) and use them as a flag that helps you divide step by step.

Why it works: For divisor D = 10^k + d (where |d| < 10^k): flag method transposes d (uses −d). Each step: bring down a digit, subtract flag×quotient-digit from remainder. The transposed coefficients generate the quotient digit by digit.

Speed advantage: Eliminates multi-digit divisor trial — reduces to single-digit operations.

Best for

• Division by numbers close to a power of 10

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Originally published at https://www.sutraflow.app/sutras/paraavartya-yojayet