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Remainder Calculator

Enter a dividend and a divisor for the quotient and the remainder, with the same answer as a mixed number and as a decimal.

Your division

The number being divided.
The number you are dividing by.
Long division
346 ÷ 7 = 49 remainder 3
Check
49 × 7 + 3 = 346
Remainder
3
Quotient
49
As a mixed number
49 3/7
As a decimal
49.4286
Divides exactly?
No — something is left over

How to use this calculator

  1. Enter the dividend — the number being divided.
  2. Enter the divisor — the number you are dividing by.
  3. Read the remainder, with the quotient beside it. The long-division line under the inputs writes the whole answer out, and the check line multiplies it back.

The mixed-number row is the same answer written as a fraction, which is what you want when the leftover matters as a quantity rather than as a count.

How to calculate a remainder

Division splits a number into as many whole groups as will fit, plus whatever is left. The remainder is that leftover.

Dividend = Quotient × Divisor + Remainder
  • Dividend — the number being divided, e.g. 346
  • Divisor — the number dividing it, e.g. 7
  • Quotient — how many whole times it fits, e.g. 49
  • Remainder — what is left over, e.g. 3

That identity is also the check. If the quotient times the divisor plus the remainder does not come back to the dividend, something has gone wrong — which is why the calculator shows the multiplication rather than only the answer.

Worked examples

Divisions in remainder and mixed-number form
DivisionQuotient and remainderAs a mixed number
346 ÷ 749 remainder 349 3/7
127 ÷ 342 remainder 142 1/3
821 ÷ 4205 remainder 1205 1/4
144 ÷ 1212 remainder 012
5 ÷ 80 remainder 55/8

A quick check while you work: a number divides by 3 or 9 exactly when the sum of its digits does. For 346 the digits add to 13, which is not a multiple of 3, so there was always going to be something left over.

Frequently asked questions

How do I find the remainder of a division?

Divide, ignore everything after the decimal point, multiply that whole number back by the divisor, then subtract it from the dividend. For 346 ÷ 7: the quotient is 49, 49 × 7 is 343, and 346 − 343 leaves a remainder of 3.

What is the difference between the quotient and the remainder?

The quotient is how many whole times the divisor fits; the remainder is what will not fit. In 346 ÷ 7 = 49 remainder 3, seven fits 49 whole times and 3 is left over. The remainder is always smaller than the divisor.

How do I write a remainder as a fraction?

Put the remainder over the divisor and attach it to the quotient. 821 ÷ 4 is 205 remainder 1, which is 205 1/4 as a mixed number, or 205.25 as a decimal. All three say the same thing.

What does a remainder of zero mean?

That the division is exact and the divisor is a factor of the dividend. 144 ÷ 12 has no remainder, so 12 divides 144 evenly. This is the standard test for divisibility.

What if the dividend is smaller than the divisor?

The quotient is zero and the whole dividend is the remainder. 5 ÷ 8 is 0 remainder 5, because eight does not fit into five even once.

How are negative numbers handled?

The quotient is truncated toward zero, so the remainder carries the sign of the dividend: −346 ÷ 7 is −49 remainder −3. That is how long division is normally taught. Modular arithmetic uses a different convention where the sign follows the divisor, which the modulo calculator covers.