Vedic maths · trick 8 of 36 · free

Dividing by 9 — Vedic maths trick

Dividing by 9 needs only adding: the quotient digits are running totals of the digits, and the remainder is the total of all of them.

The trick

Nikhilam — “all from 9 and the last from 10”

  1. Running totals of the digits, except the last, give the quotient digits.
  2. Add the last digit too — that total is the remainder.
  3. If the remainder is 9 or more, take out nines: add them to the quotient.

Use it for: Any whole number divided by 9 (and a quick way to check divisibility by 9).

Worked example: 1234 ÷ 9 = 137 remainder 1

  1. Running totals: 1, 1+2 = 3, 3+3 = 6 → quotient 136.
  2. Remainder: 6 + 4 = 10.
  3. 10 is 9 or more: quotient 136 + 1 = 137, remainder 1.
  4. Answer: 137 remainder 1.

Check: 137 × 9 + 1 = 1233 + 1 = 1234 ✓

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