CalculateY
Quick Answer
245 divided by 7 equals 35 with no remainder. 100 divided by 3 equals 33 remainder 1, or 33.333... as a repeating decimal.
Common Examples
| Input | Result |
|---|---|
| 245 / 7 | Quotient: 35, Remainder: 0 |
| 100 / 3 | Quotient: 33.333..., Remainder: 1 |
| 1000 / 13 | Quotient: 76.923076..., Remainder: 12 |
| 528 / 16 | Quotient: 33, Remainder: 0 |
| 7 / 4 | Quotient: 1.75, Remainder: 3 |
How It Works
The Long Division Algorithm
Long division is a standard procedure for dividing multi-digit numbers. It works by processing the dividend one digit at a time from left to right:
- Divide: Determine how many times the divisor fits into the current working number.
- Multiply: Multiply the divisor by the quotient digit from step 1.
- Subtract: Subtract the product from the current working number.
- Bring down: Bring down the next digit of the dividend and repeat.
When the integer portion is complete, if there is a remainder, you can continue the process by appending zeros (adding a decimal point) to compute decimal digits.
Repeating Decimals
Some divisions produce decimals that repeat forever. For example, 1/3 = 0.333… and 1/7 = 0.142857142857… A repeating decimal occurs when a remainder that has already appeared shows up again during the decimal expansion. The block of digits between those two occurrences is the repeating block, often written with a bar over the digits.
By the pigeonhole principle, a division by n can produce at most n - 1 distinct nonzero remainders before a repeat must occur. So 1/7 has a repeating block of at most 6 digits (and it does: 142857).
Worked Example
Divide 528 by 16.
Step 1: 5 / 16 = 0, remainder 5. Bring down 2 to get 52. Step 2: 52 / 16 = 3, product is 48, remainder 4. Bring down 8 to get 48. Step 3: 48 / 16 = 3, product is 48, remainder 0.
The quotient is 33 with a remainder of 0. Verification: 33 * 16 = 528.
For 100 / 3: 10 / 3 = 3, product 9, remainder 1. Bring down 0 to get 10. This is the same as before, so the decimal repeats. The quotient is 33.333… with remainder 1 and repeating block “3”.