Long division calculator
Enter a dividend and a divisor to see the division written the way it is taught on paper, with each subtraction and each digit brought down. You also get the quotient with remainder and the decimal result, with any repeating digits marked.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Type the dividend in the first box and the divisor in the second.
- Read the quotient and remainder at the top, and the decimal below them.
- Follow the layout and the numbered steps to see how each digit is found.
How it works
The algorithm goes through the dividend one digit at a time. It keeps a running remainder, appends the next digit to it, finds the largest quotient digit q with q × divisor not greater than that number, and subtracts. The decimal part continues with the final remainder: multiply it by 10, divide by the divisor to get the next digit, and keep the new remainder. When a remainder appears for the second time, the digits since its first appearance repeat forever. If the remainder reaches 0 the decimal ends.
Worked example
435 ÷ 7: 43 ÷ 7 = 6 (6 × 7 = 42, remainder 1), bring down 5 to make 15, 15 ÷ 7 = 2 (2 × 7 = 14, remainder 1). The quotient is 62 with remainder 1, so 435 = 62 × 7 + 1. Continuing with the remainder 1 gives the repeating decimal 62.(142857).
Tips
- Check your work: quotient × divisor + remainder must give the dividend.
- A remainder of 0 means the divisor divides the dividend exactly.
- The repeating block of a fraction with divisor d is never longer than d − 1 digits.
Frequently asked questions
How does long division work?
Take the leftmost digits of the dividend until they form a number at least as big as the divisor. Find how many times the divisor fits, write that digit in the quotient, subtract, and bring down the next digit. Repeat until all digits are used. What is left is the remainder.
What does the remainder mean?
It is what is left over after the last subtraction, always smaller than the divisor. The dividend equals quotient × divisor + remainder, which the Check row spells out.
Why does the decimal have brackets?
Some fractions never end. 1 ÷ 6 = 0.1666…, written 0.1(6), where the digit in brackets repeats forever. 1 ÷ 7 repeats the block 142857. Once the fraction is reduced, the decimal ends only when the divisor has no prime factors other than 2 and 5.
Can I divide decimals or negative numbers?
Not in this tool, which works with whole numbers so that the written layout stays exact. To divide decimals, multiply both numbers by the same power of 10 until they are whole.
What if the dividend is smaller than the divisor?
The quotient is 0 and the remainder is the dividend. The decimal result is still shown, for example 5 ÷ 7 = 0.(714285).