What is the Long Division Calculator?
This calculator performs long division on two numbers, returning the quotient (how many whole times the divisor fits into the dividend), the remainder (what is left over), and the exact decimal result. It is a fast way to check homework, balance counts, or split quantities into equal groups with leftovers.
How to use it
Enter the dividend (the number being divided) and the divisor (the number you divide by). Press calculate to see the quotient and remainder. The divisor cannot be zero, since dividing by zero is undefined.
The formula explained
Every division can be written as $$a = b \cdot q + r$$ where \(a\) is the dividend, \(b\) is the divisor, \(q\) is the quotient, and \(r\) is the remainder. The remainder always satisfies \(0 \le r < |b|\). The quotient is the floor of \(a \div b\), and the remainder is simply \(a - b \cdot q\).
Worked example
Divide 1234 by 7. Seven goes into 1234 a total of 176 times because \(7 \times 176 = 1232\). The remainder is \(1234 - 1232 = 2\). So the quotient is 176 with remainder 2, and the decimal result is approximately 176.2857.
FAQ
What does the remainder mean? It is the amount left over after dividing as many whole times as possible.
Can I divide negative numbers? Yes. This tool uses floor division so the remainder stays non-negative and less than the absolute value of the divisor.
Why is dividing by zero undefined? No number multiplied by zero gives a non-zero dividend, so the operation has no answer.
