100 divided by 7
Full step-by-step long division. Use the calculator below to try any other pair of numbers.
Quotient & Remainder
14 R 2
As a Decimal
14.(285714)
The digits in parentheses repeat forever.
Example
100 ÷ 7 is 14 with a remainder of 2 — or 14.(285714) as a decimal.
The dividend split into an even multiple of the divisor, plus the remainder
- 14 × 7 = 98
- Remainder: 2
What is Long Division?
Long division is the standard method for dividing large numbers by hand, one digit at a time. Rather than dividing the whole dividend at once, it works through the dividend's digits left to right — dividing, multiplying, subtracting, and bringing down the next digit — until every digit has been processed.
Step-by-Step Solution
Each row processes one digit of 100, dividing by 7.
| Step | Bring Down | Value | 7 × Digit | Product | Subtract → Remainder |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 7 × 0 | 0 | 1 − 0 = 1 |
| 2 | 10 | 10 | 7 × 1 | 7 | 10 − 7 = 3 |
| 3 | 100 | 30 | 7 × 4 | 28 | 30 − 28 = 2 |
How Does Long Division Work?
Long division repeats four steps for each digit: divide the current running value by the divisor to get one quotient digit, multiply that digit back by the divisor, subtract to find what's left over, then bring down the next digit of the dividend and repeat. Once every digit has been brought down, whatever is left over is the final remainder.
Turning the Remainder Into a Decimal
Once the whole-number digits run out, the same process continues by appending a decimal point and bringing down zeros instead of digits — each step still divides, multiplies, and subtracts exactly the same way. This is how a leftover remainder becomes the digits after the decimal point.
Why Some Decimals Repeat Forever
At every decimal step, the running remainder must be some whole number smaller than the divisor — so there are only a finite number of possible remainders. If the division doesn't terminate exactly, the same remainder is eventually guaranteed to reappear, and once it does, every digit that follows repeats in exactly the same pattern as before. This calculator detects that repeat automatically and marks the repeating block in parentheses.
Long Division vs. a Calculator's Divide Button
A basic calculator only shows the final decimal answer, rounded to however many digits fit the display — it doesn't show the remainder or the reasoning behind each digit. Long division is taught precisely because it shows the mechanism: it's how you'd verify a calculator's answer by hand, and it's the method behind polynomial division in algebra later on.
Example — Your Current Inputs
100 ÷ 7 is 14 with a remainder of 2 — or 14.(285714) as a decimal.
Additional Example — Splitting a Bill
Splitting a $137 restaurant bill evenly among 8 people: 137 ÷ 8 = 17 with a remainder of 1, or $17.125 per person exactly. In practice you'd round to $17.13 per person (rounding up slightly so the total covers the bill), since currency can't be split into thousandths of a cent.
About These Parameters
- Dividend
- The number being split up — in the expression "20 ÷ 4," the dividend is 20.
- Divisor
- The number of equal groups you're dividing into — in "20 ÷ 4," the divisor is 4. It can never be zero, since dividing by zero is undefined.
Frequently Asked Questions
What's the difference between the remainder and the decimal part?
The remainder is a whole number left over after dividing as far as whole numbers go (e.g. 17 R 1). The decimal expansion continues that same division into fractional digits instead of stopping at the remainder (e.g. 17.125). Both describe the exact same leftover amount, just in different forms.
How do I know if a decimal will repeat before calculating it?
A fraction's decimal expansion terminates exactly when the divisor (after simplifying the fraction) has no prime factors other than 2 and 5 — divisors like 8 (2³) or 20 (2²×5) terminate, while divisors like 3, 7, or 12 (which include a factor of 3) produce a repeating decimal.
Does this work with negative numbers?
This calculator is scoped to positive whole numbers to keep the step-by-step trace focused on the core algorithm. For a negative result, divide the absolute values here and apply the sign separately: the result is negative whenever exactly one of the dividend or divisor is negative.