Long Division

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:

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.