Long Division Calculator

Use four repeating steps: divide, multiply, subtract, bring down. Find how many times the divisor goes into the first part of the dividend and write that digit on top. Multiply it by the divisor, write the product underneath and subtract. Bring down the next digit beside the remainder and repeat until no digits are left; what remains is the remainder.

Divide as usual until every digit of the dividend has been brought down. The number left after the last subtraction is the remainder, and it is always smaller than the divisor. For 1234 ÷ 7 the quotient is 176 and the remainder is 2, written 176 R 2, which you can check with 7 × 176 + 2 = 1234.

Move the decimal point in the divisor to the right until it is a whole number, and move the point in the dividend the same number of places, adding zeros if needed. Both numbers are multiplied by the same power of ten, so the answer does not change. For example 4.5 ÷ 0.15 becomes 450 ÷ 15, which is 30.

When the digits run out and there is still a remainder, put a decimal point in the quotient directly above the dividend's decimal point, write a 0 after the dividend and bring it down. Keep adding zeros and dividing until the remainder is 0 or you have as many decimal places as you need. Set Decimal places above to do this automatically.

A repeating decimal is one where a block of digits repeats forever, such as 1/3 = 0.333… or 1/7 = 0.142857142857…. It is written with a bar over the repeating block, or with the block in brackets: 0.(3) and 0.(142857). It happens whenever a remainder appears for a second time during long division, because from then on the same steps repeat.

Reduce the fraction to lowest terms and look at the denominator. If its only prime factors are 2 and 5, the decimal terminates — 3/8 = 0.375 and 7/20 = 0.35. Any other prime factor, such as 3, 7 or 11, makes the decimal repeat. The calculator shows the simplified fraction so you can check this yourself.

In a ÷ b = q R r, a is the dividend (the number being divided), b is the divisor (the number you divide by), q is the quotient (the result) and r is the remainder (what is left over). In the long division layout, the divisor sits outside the bracket, the dividend inside it and the quotient on top.

Multiply the quotient by the divisor and add the remainder: the result should equal the dividend. For 98765 ÷ 123 = 802 R 119, check 123 × 802 + 119 = 98765. For a decimal answer, multiply the quotient by the divisor and you should get back the dividend, or very close to it if the decimal was rounded.

Yes. Divide the sizes of the numbers as if both were positive, then decide the sign: the answer is negative when exactly one of the two numbers is negative, and positive when both have the same sign. So −22 ÷ 7 = −3.142857… and −22 ÷ −7 = 3.142857…. This calculator applies that rule to the quotient.