Technique explanation
Flag division (Dhwajanka) splits the divisor into a 'main divisor' (first digit) and a 'flag' (remaining digits). Divide by the main divisor, then adjust the next dividend by subtracting (Flag * Latest Quotient Digit). If the result is negative, 'back off' by reducing the previous quotient digit.
This is a general method for any divisor. Standard fallback: Conventional long division.
Worked examples
Example 1: 38982 divided by 73
- Divisor: 7 (main), 3 (flag).
- Step 1: 38 / 7 = 5, rem 3. Adjusted: 39 - (53) = 24.
- Step 2: 24 / 7 = 3, rem 3. Adjusted: 38 - (33) = 29.
- Step 3: 29 / 7 = 4, rem 1. Adjusted: 12 - (43) = 0.
- Result: 534.
- Check: 534 × 73 = 38,982.
Example 2: 1234 divided by 32
- Divisor: 3 (main), 2 (flag).
- Step 1: 12 / 3 = 4, rem 0. Adjusted: 03 - (42) = -5 (Negative! Back off).
- Back off: 12 / 3 = 3, rem 3. Adjusted: 33 - (32) = 27.
- Step 2: 27 / 3 = 9, rem 0. Adjusted: 04 - (92) = -14 (Negative! Back off).
- Back off: 27 / 3 = 8, rem 3. Adjusted: 34 - (8*2) = 18.
- Result: Quotient 38, Remainder 18.
- Check: (38 × 32) + 18 = 1216 + 18 = 1234.
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