Math July 13, 2026 · 8 Min Read

Remainder Calculator – Guide & Formulas

Calculate the remainder of any division. See the quotient, remainder, and step-by-step long division for dividend ÷ divisor instantly.

Calculate the remainder of any division with our free online Remainder Calculator. Enter a dividend and divisor to see the quotient, remainder, and step-by-step long division.

Key Takeaway

Use the free Remainder Calculator to calculate the remainder of any division. see the quotient, remainder, and step-by-step long division for dividend ÷ divisor instantly. Get instant results with step-by-step explanations.

How to Use the Remainder Calculator

  1. Step 1: Enter the dividend (the number being divided)
  2. Step 2: Enter the divisor (the number you divide by)
  3. Step 3: Click Calculate to see the quotient and remainder
  4. Step 4: Review the long division steps and verification

The Formula

Division Algorithm: Dividend (a) = Divisor (b) × Quotient (q) + Remainder (r), where 0 ≤ r < |b|. The remainder r = a mod b.

Variable Definitions

  • a: The dividend — the number being divided
  • b: The divisor — the number dividing the dividend
  • q: The quotient — the integer result of a ÷ b
  • r: The remainder — what is left over after division

Finding the Remainder of 17 ÷ 5

Calculate 17 mod 5 using the division algorithm.

  1. Step 1: Divide 17 by 5: 17 ÷ 5 = 3.4
  2. Step 2: Take the integer part: quotient q = 3
  3. Step 3: Multiply divisor by quotient: 5 × 3 = 15
  4. Step 4: Subtract from dividend: 17 - 15 = 2
  5. Step 5: The remainder is 2. Verify: 5 × 3 + 2 = 17 ✓

Frequently Asked Questions

What is the remainder when a smaller number is divided by a larger number?

When dividing a smaller positive number by a larger one, the quotient is 0 and the remainder equals the dividend. For example, 3 ÷ 7 gives remainder 3.

Can the remainder be negative?

In standard math, remainders are non-negative (0 ≤ r < |b|). Some programming languages may return negative remainders for negative dividends.

What is the modulo operation?

Modulo (mod) is the same as finding the remainder. a mod b returns the remainder after dividing a by b. For example, 17 mod 5 = 2.

How do I use this for the Remainder Theorem?

The Remainder Theorem states that f(a) is the remainder when polynomial f(x) is divided by (x - a). Use this calculator for numerical verification of polynomial division.

What if the divisor is 0?

Division by zero is mathematically undefined. The calculator will display an error for zero divisors.