When the divisor has two digits (or more), you can't always
spot the answer at a glance the way
short division
lets you. Long division writes out the working in full, repeating
the same four steps for every digit of the dividend, working
left to right:
- DIVIDE — how many times does the divisor go in?
- MULTIPLY — that digit times the divisor.
- SUBTRACT — take it away to find what's left.
- BRING DOWN — drop the next digit beside the remainder.
Here is 432 \div 16 = 27 worked out in full. Read it
top to bottom; each block is one round of divide–multiply–subtract–bring down.
2 7 ← quotient (answer)
┌────────
16 │ 4 3 2
3 2 16 × 2 = 32 (DIVIDE: 43 ÷ 16 = 2, MULTIPLY)
───
1 1 2 43 − 32 = 11 (SUBTRACT), then BRING DOWN the 2 → 112
1 1 2 16 × 7 = 112 (DIVIDE: 112 ÷ 16 = 7, MULTIPLY)
─────
0 112 − 112 = 0 (SUBTRACT) — nothing left, so it divides exactly
The divisor 16 goes into 43
twice (the 4 alone is too small), then into
112 exactly seven times — giving
432 \div 16 = 27.
Often the last subtraction doesn't reach zero — there is a little left
over, the remainder.
Divide 437 by 16 instead and
the final step leaves 5:
437 \div 16 = 27 \text{ r } 5
That left-over 5 can be written as a fraction of the
divisor, 27\tfrac{5}{16}, or you can keep going past the
decimal point to turn it into 27.3125. Either way, the
remainder is always smaller than the divisor — if it weren't, the divisor
would go in one more time.
- Repeat four steps left to right: divide, multiply, subtract, bring down.
- The amount left over at the very end is the remainder (always less than the divisor).
- Check your work with \text{quotient} \times \text{divisor} + \text{remainder} = \text{dividend}.