Dividend
The dividend is the number being divided in a division problem.
Formula
\text{dividend} / \text{divisor} = \text{quotient}
Definition
The dividend is the number being divided up in a division problem; in $a / b = q$, $a$ is the dividend, $b$ is the divisor, and $q$ is the quotient. The division algorithm guarantees that for integers $a, b$ ($b > 0$), unique $q$ and $r$ exist such that $a = bq + r$ with $0 \le r < b$, so the dividend $a$ equals $bq + r$. The term extends to any element being divided in a divisibility relation: in a Euclidean domain, every pair $(a, b)$ with $b \neq 0$ yields unique $q$ and $r$ such that $a = bq + r$ where the Euclidean norm $N(r) < N(b)$.
Example
In $30 / 6 = 5$, the dividend is $30$: we are splitting $30$ into equal groups. In $47 / 8$: dividend $= 47$, divisor $= 8$, quotient $= 5$, remainder $= 7$, and checking, $8 \times 5 + 7 = 47$. In the Gaussian integers $\mathbb{Z}[i]$, dividing $7+4i$ by $3+2i$ gives $7+4i = (3+2i)(2) + (1+0i)$, so quotient $= 2$ and remainder $= 1$ (since $|1| < |3+2i| = \sqrt{13}$).
Key Insight
The dividend is the "total" you start with before sharing: it is always the number that gets divided. In long division, you work with parts of the dividend one digit at a time, using partial dividends at each step, and understanding the dividend's role is key to tracking what you have "used up." The relationship generalizes to polynomials, where in polynomial long division the dividend polynomial is divided by the divisor polynomial, yielding a quotient polynomial and a remainder of lower degree.