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Long Division Calculator

Math

Perform long division with whole numbers or decimals showing the step-by-step bracket diagram, quotient, remainder, and fractional form.

Presets:
487 ÷ 32 =
15 R 7
Decimal Quotient 15.21875
Mixed Number 15 7/32
Long Division Bracket Layout
32 15 R 7
32
487
1. Subtract 32:
-32
167
2. Subtract 160:
-160
7

Detailed Step-by-Step Instructions

Step 1

32 goes into 48 1 times (1 × 32 = 32). Subtract to get remainder 16. Bring down next digit 7.

Step 2

32 goes into 167 5 times (5 × 32 = 160). Subtract to get remainder 7.

How This Calculator Works

Long division is a standard step-by-step algorithm used for dividing multi-digit numbers. It breaks down the division into a sequence of simpler steps: Divide, Multiply, Subtract, and Bring Down (often remembered as "Daddy, Mother, Sister, Brother").

📐 Division Theorem Formula
Dividend = (Divisor × Quotient) + Remainder | 0 ≤ Remainder < Divisor
Dividend: The number being divided (inside the bracket)
Divisor: The number you are dividing by (outside the bracket)
Quotient: The whole integer answer (on top of the bracket)
Remainder: The leftover amount that cannot be divided evenly

Key Mathematical Rules & Properties

Step 1: Divide & Multiply

Examine how many times the divisor fits into the current partial dividend. Write the quotient digit above the bracket and multiply it by the divisor.

Step 2: Subtract & Compare

Subtract the multiplication result from the partial dividend. Verify the difference is strictly less than the divisor.

Step 3: Bring Down Next Digit

Bring down the next available digit of the dividend to form a new partial dividend and repeat.

Decimal Conversion

Add a decimal point and trailing zeroes to the dividend to continue dividing when a remainder remains.

✎

Worked Example: 458 ÷ 7

Divide 458 by 7 using long division.

  1. 7 does not go into 4; examine first two digits: 45.
  2. 45 ÷ 7 = 6 with a remainder. Write 6 on top.
  3. Multiply: 6 × 7 = 42. Subtract: 45 - 42 = 3.
  4. Bring down 8 to make 38.
  5. 38 ÷ 7 = 5. Write 5 on top.
  6. Multiply: 5 × 7 = 35. Subtract: 38 - 35 = 3.
  7. No more digits to bring down. Quotient is 65 with remainder 3.
Final Answer: 65 R 3 (Decimal: 65.42857...)

Frequently Asked Questions

Can the remainder ever be larger than the divisor?

No. If the subtraction step yields a number equal to or greater than the divisor, the estimated quotient digit was too small and must be increased.

What should you do when the divisor does not go into the brought-down number?

Write a 0 in the quotient for that place value, and immediately bring down the next digit.

How do you check if your long division is correct?

Multiply the quotient by the divisor and add the remainder: (Quotient × Divisor) + Remainder should exactly equal the Dividend.

How is mixed number form written from long division?

Write the whole quotient, followed by a fraction of Remainder / Divisor (e.g. 65 3/7).

Understanding your calculation

Method, example and limitations

How the calculation works

Long division finds how many times the divisor fits into successive parts of the dividend, carrying each remainder forward.

Example to check

125 ÷ 4 gives a quotient of 31 and remainder 1, equivalent to 31.25.

Before using the result

The divisor cannot be zero. A repeating decimal is an approximation when displayed with a finite number of digits; quotient-and-remainder output preserves an exact integer relationship.

Calculation methodology · Report a result that needs review