Long Division Calculator

Introduction: How to use this Long Division Calculator

1. Enter a whole-number dividend (the number being divided).
2. Enter a whole-number divisor (the number you divide by).
3. Click Calculate to see the quotient, remainder, and a step-by-step table showing each “bring down” and subtraction.

What long division computes

Long division is a standard algorithm for dividing integers that produces two outputs:

• Quotient (q): how many whole times the divisor fits into the dividend.
• Remainder (r): what is left over after taking out those whole groups.

Formula: Core relationship (division algorithm)

For integers where the divisor is nonzero, the result is defined by:

with the remainder constrained by:

0 ≤ r < |d| (and d ≠ 0).

Here D is the dividend, d is the divisor, q is the quotient, and r is the remainder.

How the step-by-step table maps to the paper method

On paper, long division works left-to-right through the digits of the dividend. At each step you:

1. Take the current partial number (often formed by “bringing down” the next digit).
2. Compute the next quotient digit as the largest integer multiple of the divisor that does not exceed that partial number.
3. Subtract that multiple to get a new remainder.
4. Bring down the next digit and repeat until all digits are used.

The calculator’s step table typically corresponds to:

• Partial Dividend: the current number being divided at that step.
• Subtract: (divisor × step-quotient-digit).
• Remainder: what remains after the subtraction (used to build the next partial dividend).

Worked example

Divide 1,652 by 7.

We are looking for integers q and r such that 1652 = 7q + r and 0 ≤ r < 7.

1. Start with 16 (first digits where 7 fits). 7 goes into 16 2 times: subtract 14, remainder 2.
2. Bring down 5 to make 25. 7 goes into 25 3 times: subtract 21, remainder 4.
3. Bring down 2 to make 42. 7 goes into 42 6 times: subtract 42, remainder 0.

So the quotient is 236 and the remainder is 0.

Example step table

Interpreting your results

• If the remainder is 0, the dividend is divisible by the divisor (an exact division).
• If the remainder is not 0, you can express the result as:
  • mixed form: q remainder r (common in grade-school long division), or
  • fraction form: q + r/d (useful for exact values), or
  • decimal: D ÷ d (may terminate or repeat).

Quick checks (to verify by multiplication)

You can verify any output by rearranging the formula:

D should equal d × q + r. If it does, the quotient and remainder are consistent.

Comparison: exact division vs remainder

Limitations and assumptions (important)

• Divisor cannot be 0. Division by zero is undefined; the calculator should reject or warn for this input.
• Integer (whole-number) long division: this page is intended for whole-number dividends and divisors. If you enter decimals, results may be rounded, truncated, or not match “paper” long division depending on implementation.
• Negative numbers: some tools treat negatives by dividing absolute values and applying the sign to the quotient. Remainder conventions vary for negatives; if you need a specific modulo convention, confirm how this calculator defines r.
• Very large integers: browsers may lose precision for extremely large values (because JavaScript numbers are floating-point). If inputs exceed safe integer limits, the quotient/remainder and step table may be inaccurate.
• Formatting: the step table is designed to mirror the standard base-10, bring-down-digit method. Alternative long-division layouts may look different but be mathematically equivalent.