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Question
What is the quotient and remainder when $ 8649 $ is divided by $ 126 $ ?
Answer
The quotient is 68 and the remainder is 81.
Explanation
|
Division Table
|
| | | | 0 | 0 | 6 | 8 |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | – | 7 | 5 | 6 | |
| | | | 1 | 0 | 8 | 9 |
| | | – | 1 | 0 | 0 | 8 |
| | | | | | 8 | 1 |
STEP 0: set up a division table
|
| | | | | | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
STEP 1: DIVIDE 8 : 126 = 0 with a remainder of 8
|
| | | | 0 | | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
STEP 2: MULTIPLY 0 · 126 = 0
|
| | | | 0 | | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | | 0 | | | |
STEP 3: SUBTRACT 8 - 0 = 8
|
| | | | 0 | | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | | | |
|
STEP 4: BRING DOWN
|
| | | | 0 | | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
STEP 5: DIVIDE 86 : 126 = 0 with a remainder of 86
|
| | | | 0 | 0 | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
STEP 6: MULTIPLY 0 · 126 = 0
|
| | | | 0 | 0 | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | | 0 | | |
STEP 7: SUBTRACT 86 - 0 = 86
|
| | | | 0 | 0 | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | | |
|
STEP 8: BRING DOWN
|
| | | | 0 | 0 | | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
STEP 9: DIVIDE 864 : 126 = 6 with a remainder of 108
|
| | | | 0 | 0 | 6 | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
STEP 10: MULTIPLY 6 · 126 = 756
|
| | | | 0 | 0 | 6 | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | | 7 | 5 | 6 | |
STEP 11: SUBTRACT 864 - 756 = 108
|
| | | | 0 | 0 | 6 | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | – | 7 | 5 | 6 | |
| | | | 1 | 0 | 8 | |
|
STEP 12: BRING DOWN
|
| | | | 0 | 0 | 6 | |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | – | 7 | 5 | 6 | |
| | | | 1 | 0 | 8 | 9 |
STEP 13: DIVIDE 1089 : 126 = 8 with a remainder of 81
|
| | | | 0 | 0 | 6 | 8 |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | – | 7 | 5 | 6 | |
| | | | 1 | 0 | 8 | 9 |
STEP 14: MULTIPLY 8 · 126 = 1008
|
| | | | 0 | 0 | 6 | 8 |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | – | 7 | 5 | 6 | |
| | | | 1 | 0 | 8 | 9 |
| | | | 1 | 0 | 0 | 8 |
STEP 15: SUBTRACT 1089 - 1008 = 81
|
| | | | 0 | 0 | 6 | 8 |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | – | 7 | 5 | 6 | |
| | | | 1 | 0 | 8 | 9 |
| | | – | 1 | 0 | 0 | 8 |
| | | | | | 8 | 1 |
STEP 15: SUBTRACT 1089 - 1008 = 81
|
| | | | 0 | 0 | 6 | 8 |
| 1 | 2 | 6 | 8 | 6 | 4 | 9 |
| | | – | 0 | | | |
| | | | 8 | 6 | | |
| | | | – | 0 | | |
| | | | 8 | 6 | 4 | |
| | | – | 7 | 5 | 6 | |
| | | | 1 | 0 | 8 | 9 |
| | | – | 1 | 0 | 0 | 8 |
| | | | | | 8 | 1 |
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