Long Division Calculator with Remainder

About the Long Division Calculator with Remainder

Long division breaks down a division problem into a sequence of simple steps, dividing the dividend by the divisor to produce a whole-number quotient and a remainder.

This Long Division Calculator computes the exact quotient and remainder (Q R r), verifies the division using the Euclidean division identity, and converts the result into a mixed fraction and decimal.

Euclidean Division & Remainder Formula

For any dividend N and non-zero divisor D:

How to Do Long Division with Remainders

1. Divide: Determine how many whole times the divisor D fits into the dividend N without going over. This integer is your quotient Q.
2. Multiply: Multiply the whole quotient Q by the divisor D.
3. Subtract: Subtract (Q × D) from the dividend N. The leftover amount is your remainder R.

Worked Example: For 100 ÷ 7, 7 goes into 100 fourteen times (7 × 14 = 98). Subtracting gives 100 − 98 = 2. Thus, 100 ÷ 7 = 14 R 2 (or 14 2/7).

Frequently Asked Questions (FAQ)

Can the remainder ever be larger than or equal to the divisor?

No. The remainder must always be strictly less than the divisor (0 ≤ R < D). If it were larger, the divisor could fit into the dividend at least one more whole time.

How do you turn a remainder into a fraction or decimal?

Place the remainder over the original divisor to form the fractional part (Q R/D), or continue dividing R ÷ D to get the decimal digits.