Long division

Long division is a written algorithm for dividing numbers by processing their digits in sequence. It records successive estimates, products, and remainders to find a quotient.

Division algorithm: A procedure that expresses an integer dividend as a divisor times a quotient plus a remainder. Long division carries out this quotient-and-remainder decomposition one digit at a time.
Division: An arithmetic operation that determines how many times one quantity is contained in another. Long division is a written procedure for carrying out this operation.
Polynomial long division: An algorithm that divides one polynomial by another by repeatedly canceling leading terms. It adapts the digit-by-digit procedure to powers of a variable.
Short division: A compact written division method that omits some intermediate products and subtraction steps. It performs similar digit-by-digit work with less written detail.
Partial quotient: A portion of a final quotient found by subtracting a multiple of the divisor from the current dividend. Each estimate contributes a place-value part to the quotient.
Multiplication: An arithmetic operation that combines equal-sized groups or scales one quantity by another. Each quotient estimate is checked by multiplying it by the divisor.
Synthetic division: A compact method for dividing a polynomial by a linear factor of the form x minus a constant. It streamlines polynomial long division when the divisor has this special form.
Partial quotients method: A division method that repeatedly subtracts convenient multiples of the divisor and adds the resulting quotient parts. It makes quotient estimates flexible instead of requiring one digit at each stage.
Remainder: The amount left after one quantity is divided by another, when division does not come out evenly. The remainder from one step is combined with the next digit.
Subtraction: An arithmetic operation that finds the difference between quantities or removes one quantity from another. Subtracting each product reveals what remains for the next step.

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