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Home/Formula Library/Long division

Long division

Divide integers with a quotient and remainder (or decimal expansion).

General

  • Percentage proportion
  • Percent error
  • Ratio and proportion
  • Rounding
  • Exponentiation
  • Nth root
  • Fraction arithmetic
  • Long division
  • Order of operations (PEMDAS)

Formula

dividend = quotient × divisor + remainder

Explanation

Long division repeatedly subtracts multiples of the divisor from the dividend. The identity dividend = quotient×divisor + remainder always holds, with 0 ≤ remainder < |divisor|. Repeating decimals appear when the remainder cycle repeats.

Variables

  • dividendnumber being divided
  • divisornumber you divide by
  • quotientwhole-number result of division
  • remainderleftover after forming the quotient

When to use

Classroom division, converting improper fractions, and checking modular arithmetic.

Use this formula

Calculators

  • Long Division Calculator→

Related formulas

  • Fraction arithmetica/b ± × ÷ c/d → reduced form
  • Order of operations (PEMDAS)PEMDAS: ( ) then × ÷ then + −

Other categories

  • Statistics
  • Cooking & apparel
  • Data & digital
  • Electricity & magnetism
  • Encodings & numbers
  • Date & time
Formula Library→

Popular

  • Percentage proportion
  • Arithmetic and weighted mean
  • Exponentiation
  • Fraction arithmetic
Formula Library→