Question
What is the quotient and remainder when $ 3084 $ is divided by $ 71 $ ?
Answer
The quotient is 43 and the remainder is 31.
Explanation
| Division Table | |||||
| 0 | 0 | 4 | 3 | ||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| – | 2 | 8 | 4 | ||
| 2 | 4 | 4 | |||
| – | 2 | 1 | 3 | ||
| 3 | 1 | ||||
|
STEP 0: set up a division table |
|||||
| 7 | 1 | 3 | 0 | 8 | 4 |
|
STEP 1: DIVIDE 3 : 71 = 0 with a remainder of 3 |
|||||
| 0 | |||||
| 7 | 1 | 3 | 0 | 8 | 4 |
|
STEP 2: MULTIPLY 0 · 71 = 0 |
|||||
| 0 | |||||
| 7 | 1 | 3 | 0 | 8 | 4 |
| 0 | |||||
|
STEP 3: SUBTRACT 3 - 0 = 3 |
|||||
| 0 | |||||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | |||||
| STEP 4: BRING DOWN | |||||
| 0 | |||||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
|
STEP 5: DIVIDE 30 : 71 = 0 with a remainder of 30 |
|||||
| 0 | 0 | ||||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
|
STEP 6: MULTIPLY 0 · 71 = 0 |
|||||
| 0 | 0 | ||||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| 0 | |||||
|
STEP 7: SUBTRACT 30 - 0 = 30 |
|||||
| 0 | 0 | ||||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | ||||
| STEP 8: BRING DOWN | |||||
| 0 | 0 | ||||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
|
STEP 9: DIVIDE 308 : 71 = 4 with a remainder of 24 |
|||||
| 0 | 0 | 4 | |||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
|
STEP 10: MULTIPLY 4 · 71 = 284 |
|||||
| 0 | 0 | 4 | |||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| 2 | 8 | 4 | |||
|
STEP 11: SUBTRACT 308 - 284 = 24 |
|||||
| 0 | 0 | 4 | |||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| – | 2 | 8 | 4 | ||
| 2 | 4 | ||||
| STEP 12: BRING DOWN | |||||
| 0 | 0 | 4 | |||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| – | 2 | 8 | 4 | ||
| 2 | 4 | 4 | |||
|
STEP 13: DIVIDE 244 : 71 = 3 with a remainder of 31 |
|||||
| 0 | 0 | 4 | 3 | ||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| – | 2 | 8 | 4 | ||
| 2 | 4 | 4 | |||
|
STEP 14: MULTIPLY 3 · 71 = 213 |
|||||
| 0 | 0 | 4 | 3 | ||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| – | 2 | 8 | 4 | ||
| 2 | 4 | 4 | |||
| 2 | 1 | 3 | |||
|
STEP 15: SUBTRACT 244 - 213 = 31 |
|||||
| 0 | 0 | 4 | 3 | ||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| – | 2 | 8 | 4 | ||
| 2 | 4 | 4 | |||
| – | 2 | 1 | 3 | ||
| 3 | 1 | ||||
|
STEP 15: SUBTRACT 244 - 213 = 31 |
|||||
| 0 | 0 | 4 | 3 | ||
| 7 | 1 | 3 | 0 | 8 | 4 |
| – | 0 | ||||
| 3 | 0 | ||||
| – | 0 | ||||
| 3 | 0 | 8 | |||
| – | 2 | 8 | 4 | ||
| 2 | 4 | 4 | |||
| – | 2 | 1 | 3 | ||
| 3 | 1 | ||||
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