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Question
What is the quotient and remainder when $ 76287 $ is divided by $ 287 $ ?
Answer
The quotient is 265 and the remainder is 232.
Explanation
|
Division Table
|
| | | | 0 | 0 | 2 | 6 | 5 |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | – | 1 | 7 | 2 | 2 | |
| | | | | 1 | 6 | 6 | 7 |
| | | | – | 1 | 4 | 3 | 5 |
| | | | | | 2 | 3 | 2 |
STEP 0: set up a division table
|
| | | | | | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
STEP 1: DIVIDE 7 : 287 = 0 with a remainder of 7
|
| | | | 0 | | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
STEP 2: MULTIPLY 0 · 287 = 0
|
| | | | 0 | | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | | 0 | | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | | | 0 | | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | | | | |
|
STEP 4: BRING DOWN
|
| | | | 0 | | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
STEP 5: DIVIDE 76 : 287 = 0 with a remainder of 76
|
| | | | 0 | 0 | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
STEP 6: MULTIPLY 0 · 287 = 0
|
| | | | 0 | 0 | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | | 0 | | | |
STEP 7: SUBTRACT 76 - 0 = 76
|
| | | | 0 | 0 | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | | | |
|
STEP 8: BRING DOWN
|
| | | | 0 | 0 | | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
STEP 9: DIVIDE 762 : 287 = 2 with a remainder of 188
|
| | | | 0 | 0 | 2 | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
STEP 10: MULTIPLY 2 · 287 = 574
|
| | | | 0 | 0 | 2 | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | | 5 | 7 | 4 | | |
STEP 11: SUBTRACT 762 - 574 = 188
|
| | | | 0 | 0 | 2 | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | | |
|
STEP 12: BRING DOWN
|
| | | | 0 | 0 | 2 | | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
STEP 13: DIVIDE 1888 : 287 = 6 with a remainder of 166
|
| | | | 0 | 0 | 2 | 6 | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
STEP 14: MULTIPLY 6 · 287 = 1722
|
| | | | 0 | 0 | 2 | 6 | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | | 1 | 7 | 2 | 2 | |
STEP 15: SUBTRACT 1888 - 1722 = 166
|
| | | | 0 | 0 | 2 | 6 | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | – | 1 | 7 | 2 | 2 | |
| | | | | 1 | 6 | 6 | |
|
STEP 16: BRING DOWN
|
| | | | 0 | 0 | 2 | 6 | |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | – | 1 | 7 | 2 | 2 | |
| | | | | 1 | 6 | 6 | 7 |
STEP 17: DIVIDE 1667 : 287 = 5 with a remainder of 232
|
| | | | 0 | 0 | 2 | 6 | 5 |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | – | 1 | 7 | 2 | 2 | |
| | | | | 1 | 6 | 6 | 7 |
STEP 18: MULTIPLY 5 · 287 = 1435
|
| | | | 0 | 0 | 2 | 6 | 5 |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | – | 1 | 7 | 2 | 2 | |
| | | | | 1 | 6 | 6 | 7 |
| | | | | 1 | 4 | 3 | 5 |
STEP 19: SUBTRACT 1667 - 1435 = 232
|
| | | | 0 | 0 | 2 | 6 | 5 |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | – | 1 | 7 | 2 | 2 | |
| | | | | 1 | 6 | 6 | 7 |
| | | | – | 1 | 4 | 3 | 5 |
| | | | | | 2 | 3 | 2 |
STEP 19: SUBTRACT 1667 - 1435 = 232
|
| | | | 0 | 0 | 2 | 6 | 5 |
| 2 | 8 | 7 | 7 | 6 | 2 | 8 | 7 |
| | | – | 0 | | | | |
| | | | 7 | 6 | | | |
| | | | – | 0 | | | |
| | | | 7 | 6 | 2 | | |
| | | – | 5 | 7 | 4 | | |
| | | | 1 | 8 | 8 | 8 | |
| | | – | 1 | 7 | 2 | 2 | |
| | | | | 1 | 6 | 6 | 7 |
| | | | – | 1 | 4 | 3 | 5 |
| | | | | | 2 | 3 | 2 |
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