Enter Your Division Problem
Whole numbers only — dividend ÷ divisor
Number being divided
Number to divide by
Decimal places:
Examples:
How to Do Long Division Step by Step
Long division uses four repeating steps to break a large division problem into manageable pieces. The pattern is: Divide → Multiply → Subtract → Bring Down. Repeat until all digits are processed.
Step 1: DIVIDE — how many times does divisor fit into current digits?
Step 2: MULTIPLY — quotient digit × divisor
Step 3: SUBTRACT — current portion − product
Step 4: BRING DOWN — bring next digit of dividend
Repeat until done → write remainder if any
Step 2: MULTIPLY — quotient digit × divisor
Step 3: SUBTRACT — current portion − product
Step 4: BRING DOWN — bring next digit of dividend
Repeat until done → write remainder if any
Long Division Example: 847 ÷ 7
- 7 goes into 8 → 1 time. Write 1 above. Multiply: 1×7=7. Subtract: 8−7=1.
- Bring down 4 → 14. 7 goes into 14 → 2 times. Multiply: 2×7=14. Subtract: 14−14=0.
- Bring down 7 → 7. 7 goes into 7 → 1 time. Multiply: 1×7=7. Subtract: 7−7=0.
- Result: 847 ÷ 7 = 121, Remainder 0. Verify: 121×7+0=847 ✓
Long Division with Remainder
When a number doesn't divide evenly, you get a remainder. Example: 17 ÷ 5 = 3 remainder 2. Write as: 3 R 2, or as fraction: 3²⁄₅, or as decimal: 3.4. The remainder is always less than the divisor.
How to Check Long Division
Quotient × Divisor + Remainder = Dividend
Example: 17 ÷ 5 = 3 R 2 → 3 × 5 + 2 = 17 ✓
Example: 17 ÷ 5 = 3 R 2 → 3 × 5 + 2 = 17 ✓
Long Division Tips for Students
- Remember DMSB: Divide, Multiply, Subtract, Bring Down — the 4 steps in order
- If divisor is too big: Look at more digits of the dividend until you have a number the divisor fits into
- Remainder must be less than divisor: If your remainder ≥ divisor, you can divide one more time
- Write a 0: If the divisor doesn't fit into current digits, write 0 in quotient and bring down next digit
- Check your work: Always verify: Quotient × Divisor + Remainder = Dividend
Long Division Common Examples
847 ÷ 7 = 121 (no remainder) ✓
17 ÷ 5 = 3 R 2 = 3²⁄₅ = 3.4
1234 ÷ 12 = 102 R 10 = 102⁵⁄₆
7 ÷ 4 = 1 R 3 = 1¾ = 1.75
17 ÷ 5 = 3 R 2 = 3²⁄₅ = 3.4
1234 ÷ 12 = 102 R 10 = 102⁵⁄₆
7 ÷ 4 = 1 R 3 = 1¾ = 1.75
When is Long Division Used?
- School math: 4th grade and 5th grade standard — dividing 2, 3, and 4-digit numbers
- Fractions: Converting improper fractions to mixed numbers
- Algebra: Polynomial long division uses the same algorithm
- Real life: Splitting costs, calculating per-unit price, dividing groups equally
Remainder as Fraction and Decimal
When a division has a remainder, there are three ways to express it:
17 ÷ 5 = 3 R 2 (remainder form)
17 ÷ 5 = 3²⁄₅ (mixed number form)
17 ÷ 5 = 3.4 (decimal form)
17 ÷ 5 = 3²⁄₅ (mixed number form)
17 ÷ 5 = 3.4 (decimal form)
This calculator shows all three forms automatically. The fraction is always simplified using the Greatest Common Factor (GCF).
Long Division vs Short Division
- Short division: Mental math method, works for simple single-digit divisors, no written steps
- Long division: Written algorithm showing all steps — works for any size divisor, required for multi-digit division
- Both give the same answer — long division is preferred for learning and checking work
Related Calculators
Also check our GCF and LCM Calculator, Fraction Calculator, Prime Factorization Calculator, Mean Median Mode Calculator, and all Math Calculators on CalcVelo.