Long Division Calculator

Long division is the pencil-and-paper method for dividing large numbers by breaking the problem into a sequence of small divisions, one digit at a time. The calculator lays out each step: which part of the dividend is being divided, the next digit of the quotient, the multiplication and the subtraction that leaves the carry for the next step. For the default problem, 100 ÷ 7, the answer is 14 with a remainder of 2, which as a decimal is 14.285714285714…, with the six digits 285714 repeating forever.

In most of the world long division is written with a bracket-shaped symbol, the dividend under it, the divisor to its left and the quotient on top, as in the diagram. Some countries put the divisor on the right or write the quotient below, but the arithmetic is the same.

Components of division

Every division problem has four named parts. The dividend is the number being divided up. The divisor is the number you divide by, the size or number of the groups. The quotient is the number of times the divisor fits completely into the dividend, and the remainder is what is left over, which is always smaller than the divisor.

The four are tied together by one equation: dividend = divisor × quotient + remainder. For 100 ÷ 7, that is 100 = 7 × 14 + 2. This makes division easy to check, and the calculator does that check for you. When the remainder is zero, the divisor is a factor of the dividend and the division is exact.

There are several ways to write the answer. As a quotient and remainder, 100 ÷ 7 = 14 R 2. As a mixed number, the remainder becomes a fraction of the divisor: 14 2/7. As a decimal, the division keeps going past the decimal point by adding zeros to the remainder, giving 14.285714… Which form is best depends on the question: if 100 cookies are shared among 7 children, each gets 14 and 2 are left over, but if 100 liters of water fill 7 tanks equally, each tank holds about 14.29 liters.

Division of a whole number by a whole number produces either a terminating decimal or a repeating one. It terminates only when the divisor, after canceling common factors with the dividend, has no prime factors other than 2 and 5. Dividing by 7, 3, 11 or 13 always gives a repeating pattern unless the division is exact.

How to perform long division?

Long division repeats four steps, often remembered as divide, multiply, subtract and bring down, until there are no digits left to bring down. Here is 8,542 ÷ 6 worked step by step.

• Start with the leftmost digits of the dividend that make a number at least as big as the divisor. 8 is bigger than 6, so start with 8.
• Divide: 6 goes into 8 once. Write 1 in the quotient above the 8.
• Multiply: 1 × 6 = 6. Write it under the 8.
• Subtract: 8 − 6 = 2. The result must be smaller than the divisor; if it is not, the quotient digit was too small.
• Bring down the next digit, 5, to make 25. Divide: 6 goes into 25 four times. Multiply: 4 × 6 = 24. Subtract: 25 − 24 = 1.
• Bring down 4 to make 14. 6 goes into 14 twice; 2 × 6 = 12, and 14 − 12 = 2.
• Bring down the last digit, 2, to make 22. 6 goes into 22 three times; 3 × 6 = 18, and 22 − 18 = 4.
• No digits remain, so the quotient is 1,423 and the remainder is 4. Check: 6 × 1,423 + 4 = 8,542.

If a brought-down number is smaller than the divisor, the quotient digit is 0, and you must still write that 0 before bringing down the next digit. Forgetting it is the most common long division mistake: 618 ÷ 6 is 103, not 13.

To continue past the decimal point, put a decimal point after the quotient, add a 0 to the remainder and keep dividing. When a remainder repeats, the digits from that point on repeat too, which is how the calculator spots the repeating block.

Frequently asked questions