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.

Long Division Example: 847 ÷ 7

1. 7 goes into 8 → 1 time. Write 1 above. Multiply: 1×7=7. Subtract: 8−7=1.
2. Bring down 4 → 14. 7 goes into 14 → 2 times. Multiply: 2×7=14. Subtract: 14−14=0.
3. Bring down 7 → 7. 7 goes into 7 → 1 time. Multiply: 1×7=7. Subtract: 7−7=0.
4. 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

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

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:

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

Long Division with 2-Digit Divisors

The same DMSB steps apply for 2-digit divisors. Example: 1234 ÷ 12

1. 12 goes into 12 → 1 time. 1×12=12. 12−12=0.
2. Bring down 3 → 3. 12 goes into 3 → 0 times. Write 0.
3. Bring down 4 → 34. 12 goes into 34 → 2 times. 2×12=24. 34−24=10.
4. Answer: 102 R 10 = 102 and 5/6

Common Long Division Examples

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