Free Long Division Calculator

Enter a dividend and divisor — see the complete worked-out solution exactly as you'd write it on paper, with every step explained.

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How Long Division Works — The DMSB Method

Every step in long division follows the same four actions, in the same order. Many teachers use the mnemonic "Daddy, Mother, Sister, Brother" or "Does McDonald's Sell Burgers?" to help kids remember:

  1. Divide — How many times does the divisor go into the current chunk?
  2. Multiply — Multiply that quotient digit by the divisor.
  3. Subtract — Subtract the product from the chunk.
  4. Bring down — Bring down the next digit of the dividend.

Repeat these four steps until you've used every digit of the dividend. What's left over is the remainder.

Example: 375 ÷ 5

  1. Divide: 5 doesn't go into 3 (3 is smaller than 5), so look at 37. 5 × 7 = 35, so 5 goes into 37 seven times.
  2. Multiply: Write 7 above the 7 in 375. Multiply: 7 × 5 = 35.
  3. Subtract: 37 − 35 = 2.
  4. Bring down: Bring down the 5 from 375. Now we have 25.
  5. Repeat: 5 goes into 25 five times. 5 × 5 = 25. Subtract: 25 − 25 = 0. No more digits to bring down.
  6. Answer: 75 with no remainder.

Common Long Division Mistakes

  • Forgetting to write a 0 in the quotient. If the divisor doesn't go into a chunk, you still need to write 0 above that digit before bringing down the next one. Skipping zeros creates a wrong answer.
  • Mixing up multiply and subtract. Always multiply first, then subtract. Trying to do them in the wrong order leads to errors.
  • Bringing down too many digits at once. Bring down ONE digit at a time, divide, then bring down the next. Don't skip steps.
  • Forgetting the remainder. If the last subtraction doesn't equal zero, the leftover is the remainder. Don't drop it.
  • Lining up digits wrong. Each quotient digit goes directly above the dividend digit you used to make that division. Use grid paper if alignment is tricky.

Frequently Asked Questions

When should I show a remainder vs a decimal?

It depends on what you're dividing. Remainder makes sense for whole-number contexts: 17 cookies divided among 5 friends = 3 cookies each with 2 left over. Decimal makes sense for measurements: 17 inches divided into 5 equal parts = 3.4 inches each. In school, Grade 4-5 typically uses remainders; Grade 6+ moves to decimals.

What grade learns long division?

Long division is typically introduced in Grade 4 with single-digit divisors (e.g., 256 ÷ 4) and extended in Grade 5 to two-digit divisors (e.g., 4,872 ÷ 12). By Grade 6, students should be fluent with all standard long division.

Why is long division so hard for kids?

Long division combines four operations (estimating, multiplying, subtracting, and place value) in a strict sequence. Each step must be done correctly for the next to work. Most struggles come from one of three things: weak multiplication facts, careless alignment, or forgetting to write zeros in the quotient.

What's the largest division this calculator handles?

You can enter up to a 6-digit dividend and a 3-digit divisor (e.g., 999,999 ÷ 999). Very large numbers can produce a worked-out solution with many steps — that's normal. The calculator will always show every step.

Why does the quotient sometimes start with a "0"?

If the divisor doesn't go into the first digit of the dividend, the quotient effectively starts with a leading 0 — but we don't write that 0 in the final answer. For example, in 375 ÷ 5, we don't write "075" — we write "75". The calculator shows the visual layout starting where the first real quotient digit goes.