Long Division Calculator
Perform long division with step-by-step work shown. See quotient, remainder, and decimal results with full explanation.
Division Result
Quotient
67
Remainder 6
Division Input
Answer Formats
With Remainder
67 R 6
Decimal
67.260870
Mixed Number
67 6/23
Step-by-Step Solution
Step 1
Current number: 154
How many times does 23 go into 154? 6 times
Multiply: 23 × 6 = 138
Subtract: 154 - 138 = 16
Step 2
Current number: 167
How many times does 23 go into 167? 7 times
Multiply: 23 × 7 = 161
Subtract: 167 - 161 = 6
Final Answer
1547 ÷ 23 = 67 with remainder 6
Verification
Check: Dividend = (Divisor × Quotient) + Remainder
1547 = (23 × 67) + 6
1547 = 1541 + 6
1547 = 1547 ✓
Quick Reference: 23 Times Table
23×1
23
23×2
46
23×3
69
23×4
92
23×5
115
23×6
138
23×7
161
23×8
184
23×9
207
23×10
230
Long Division Tips
- •DMSB: Divide, Multiply, Subtract, Bring down - repeat this pattern
- •Estimate first: Know your multiplication tables to quickly find quotient digits
- •Check subtraction: Remainder must be less than divisor
- •Verify your answer: (Divisor × Quotient) + Remainder = Dividend
?How Do You Do Long Division?
Long division breaks down division into steps: divide, multiply, subtract, bring down. For 156 / 12: 12 goes into 15 once (15-12=3), bring down 6, 12 goes into 36 three times exactly. Result: 13 with remainder 0. Long division shows the complete process for learning and verification.
What is Long Division?
Long division is a standard procedure for dividing multi-digit numbers that breaks the process into a series of easier steps. It systematically divides, multiplies, subtracts, and brings down digits until the entire dividend is processed, yielding a quotient and possibly a remainder.
Key Facts About Long Division
- Steps: Divide, Multiply, Subtract, Bring down (DMSB)
- Dividend / Divisor = Quotient with Remainder
- Check: (Quotient x Divisor) + Remainder = Dividend
- Remainder must be less than divisor
- Can continue past decimal for exact division
- Works for integers and decimals
- Foundation for polynomial division
- Essential arithmetic skill for understanding division
Quick Answer
Long division breaks down division into steps: divide, multiply, subtract, bring down. For 156 / 12: 12 goes into 15 once (15-12=3), bring down 6, 12 goes into 36 three times exactly. Result: 13 with remainder 0. Long division shows the complete process for learning and verification.
Frequently Asked Questions
Long division follows DMSB: Divide (how many times divisor fits), Multiply (divisor × quotient digit), Subtract (from current dividend), Bring down (next digit). Repeat until all digits are processed. The final subtraction gives the remainder.
The quotient is how many times the divisor fits completely into the dividend. The remainder is what's left over. For 17÷5: quotient is 3 (5×3=15), remainder is 2 (17-15=2). We write: 17÷5 = 3 R 2 or 17 = 5×3 + 2.
Verify using: Dividend = (Divisor × Quotient) + Remainder. For 47÷6 = 7 R 5: Check 6×7+5 = 42+5 = 47 ✓. The remainder must always be less than the divisor.
If the divisor is larger than the current digit(s), write 0 in the quotient and bring down the next digit. For 105÷5: 5 doesn't fit in 1, so we use 10. 5 fits in 10 twice (10÷5=2). Continue with remaining digits.
To continue division past the decimal point, add a decimal to the quotient and zeros to the dividend. Continue dividing. For 17÷4: 17÷4=4 R 1, add .0 to get 10÷4=2 R 2, then 20÷4=5. Result: 4.25.
Last updated: 2025-01-15
Division Result
Quotient
67
Remainder 6