Result
31 R 1
Decimal
31.25
Exact
No
Number of decimal places to show in the decimal result (1-20).
31
1
31.25
125/4
31 1/4
31 × 4 + 1 = 125
a = q × b + r, where 0 ≤ r < bEvery integer a divided by positive integer b produces a unique quotient q and remainder r.
Where:
a= Dividend (number being divided)b= Divisor (number dividing by)q= Quotient (whole number result)r= Remainder (0 ≤ r < b)a / b = q + r/b = q.ddd...The decimal result equals the quotient plus the remainder divided by the divisor.
Where:
a/b= Division expressed as fractionq= Integer quotientr/b= Fractional partInputs
Result
Step 1: 1 ÷ 4 = 0 R1. Step 2: 12 ÷ 4 = 3 R0. Step 3: 5 ÷ 4 = 1 R1. Quotient = 31, Remainder = 1. Verify: 31 × 4 + 1 = 125.
Inputs
Result
1000 ÷ 7: 1 ÷ 7 = 0 R1, 10 ÷ 7 = 1 R3, 30 ÷ 7 = 4 R2, 20 ÷ 7 = 2 R6. Quotient = 142, Remainder = 6. Verify: 142 × 7 + 6 = 1000.
Inputs
Result
256 ÷ 16: 25 ÷ 16 = 1 R9, 96 ÷ 16 = 6 R0. Quotient = 16, Remainder = 0. This is an exact division.
Long division breaks a division problem into a series of smaller steps. For each digit of the dividend, you divide, multiply, subtract, and bring down the next digit. For example, 125 ÷ 4: first 1 ÷ 4 = 0 R1, bring down 2 to get 12, then 12 ÷ 4 = 3, then bring down 5 to get 5, and 5 ÷ 4 = 1 R1.
| Division | Quotient | Remainder | Decimal |
|---|---|---|---|
| 125 ÷ 4 | 31 | 1 | 31.25 |
| 1000 ÷ 7 | 142 | 6 | 142.857... |
| 256 ÷ 16 | 16 | 0 | 16.0 |
| 99 ÷ 8 | 12 | 3 | 12.375 |
The quotient is the whole number result of division, while the remainder is what is left over. In 125 ÷ 4 = 31 R1, the quotient is 31 and the remainder is 1. Together they satisfy: dividend = quotient × divisor + remainder, so 125 = 31 × 4 + 1.
| Term | Symbol | In 125 ÷ 4 |
|---|---|---|
| Dividend | a | 125 |
| Divisor | b | 4 |
| Quotient | q | 31 |
| Remainder | r | 1 |
Any division a ÷ b can be written as the fraction a/b. Simplify by dividing both by their GCD. For a mixed number, the whole part is the quotient and the fraction part is remainder/divisor. Example: 125 ÷ 4 = 125/4 = 31 1/4.
| Division | Fraction | Simplified | Mixed Number |
|---|---|---|---|
| 125 ÷ 4 | 125/4 | 125/4 | 31 1/4 |
| 36 ÷ 8 | 36/8 | 9/2 | 4 1/2 |
| 100 ÷ 6 | 100/6 | 50/3 | 16 2/3 |
Yes. After reaching the last digit, if there is a remainder, you add a decimal point and continue dividing by appending zeros. For 125 ÷ 4, after getting quotient 31 with remainder 1, you append .0 to get 10, and 10 ÷ 4 = 2 R2, giving 31.25 after one more step.
| Division | Decimal | Type |
|---|---|---|
| 125 ÷ 4 | 31.25 | Terminating |
| 1 ÷ 3 | 0.333... | Repeating |
| 22 ÷ 7 | 3.142857... | Repeating |
| 256 ÷ 16 | 16.0 | Exact |
Long division builds number sense and understanding of place value, remainders, and the relationship between multiplication and division. It is the foundation for polynomial division in algebra, converting fractions to decimals, and understanding how computers perform division internally.
| Application | Uses Long Division | Level |
|---|---|---|
| Fraction to decimal | Divide numerator by denominator | Elementary |
| Polynomial division | Same algorithm with variables | Algebra |
| Modular arithmetic | Finding remainders | Number theory |
| Computer science | Binary division circuits | Advanced |
Read our guide
Add, subtract, multiply, and divide fractions
Perform arithmetic with mixed numbers
Calculate percentages and proportions
Find greatest common divisor and least common multiple
Last Updated: Mar 9, 2026
This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.