Long Division Calculator

Bring down one digit at a time, see how many times the divisor fits into the running partial, write that digit in the quotient, subtract, and repeat with what is left.

What is left over when the divisor no longer fits a whole number of times. 1234 divided by 7 gives 176 with a remainder of 2, since 176 × 7 = 1232.

Multiply the quotient by the divisor and add the remainder — it should give back the dividend exactly. It is the fastest check there is and it catches almost every error.

A fraction terminates only when the reduced denominator's prime factors are just 2 and 5, which are the primes dividing ten. Sevenths, thirds and ninths never terminate however far you carry the division.

It is undefined. There is no number that multiplied by zero gives a non-zero result, so the question has no answer rather than an infinite one.

As a procedure for dividing large numbers, rarely. As a demonstration of place value and of what division actually does, it remains one of the clearest things in arithmetic.

The same process with the intermediate subtractions done mentally, written as a single line with carries. It is quicker for small divisors and harder to check.

Shift both numbers by the same power of ten until the divisor is a whole number, then divide normally. Dividing by 0.25 is the same as multiplying by 4.

The remainder is what is left over in whole-number division; the decimal continues the division past the point. Both describe the same result and answer different questions.

At most one less than the divisor. Sevenths repeat with a six-digit cycle — 0.142857 — which is the longest possible for 7.

Because 3 does not divide any power of ten. A fraction terminates only when the reduced denominator's prime factors are 2 and 5, the primes that divide ten.

The notation varies considerably — the placement of the divisor, the bracket shape and whether subtractions are written out all differ by country. The arithmetic is identical.