In more detail
17 ÷ 5 is a quotient of 3 with a remainder of 2, because 3 × 5 + 2 = 17. Long division repeats four steps from the leftmost digit: divide, multiply, subtract, bring down the next digit. Each remainder must be smaller than the divisor; if it is not, the quotient digit was too small. The result always satisfies dividend = divisor × quotient + remainder.
Why it matters
It is the method behind dividing by hand, checking a calculator, and arbitrary-precision arithmetic in software, which divides numbers too big for hardware in the same digit-by-digit way. The remainder is what Modulo returns, and continuing past the last digit with zeros produces decimals; a remainder that recurs means the decimal repeats.
Example
7,345 ÷ 12:
73 ÷ 12 = 6 6 × 12 = 72 73 − 72 = 1 bring down 4 → 14
14 ÷ 12 = 1 1 × 12 = 12 14 − 12 = 2 bring down 5 → 25
25 ÷ 12 = 2 2 × 12 = 24 25 − 24 = 1
quotient 612, remainder 1 check: 612 × 12 + 1 = 7,345
Continuing with zeros: 10 ÷ 12 = 0 r 10, then 100 ÷ 12 = 8 r 4, then 40 ÷ 12 = 3 r 4, and the remainder 4 repeats, so 7,345 / 12 = 612.08333…