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Question
What is the quotient and remainder when $ 4166 $ is divided by $ 14 $ ?
Answer
The quotient is 297 and the remainder is 8.
Explanation
|
Division Table
|
| | | 0 | 2 | 9 | 7 |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 0 | 6 |
| | | | – | 9 | 8 |
| | | | | | 8 |
STEP 0: set up a division table
|
| | | | | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
STEP 1: DIVIDE 4 : 14 = 0 with a remainder of 4
|
| | | 0 | | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
STEP 2: MULTIPLY 0 · 14 = 0
|
| | | 0 | | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | | 0 | | | |
STEP 3: SUBTRACT 4 - 0 = 4
|
| | | 0 | | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
STEP 5: DIVIDE 41 : 14 = 2 with a remainder of 13
|
| | | 0 | 2 | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
STEP 6: MULTIPLY 2 · 14 = 28
|
| | | 0 | 2 | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | | 2 | 8 | | |
STEP 7: SUBTRACT 41 - 28 = 13
|
| | | 0 | 2 | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
STEP 9: DIVIDE 136 : 14 = 9 with a remainder of 10
|
| | | 0 | 2 | 9 | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
STEP 10: MULTIPLY 9 · 14 = 126
|
| | | 0 | 2 | 9 | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | | 1 | 2 | 6 | |
STEP 11: SUBTRACT 136 - 126 = 10
|
| | | 0 | 2 | 9 | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 0 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 9 | |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 0 | 6 |
STEP 13: DIVIDE 106 : 14 = 7 with a remainder of 8
|
| | | 0 | 2 | 9 | 7 |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 0 | 6 |
STEP 14: MULTIPLY 7 · 14 = 98
|
| | | 0 | 2 | 9 | 7 |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 0 | 6 |
| | | | | 9 | 8 |
STEP 15: SUBTRACT 106 - 98 = 8
|
| | | 0 | 2 | 9 | 7 |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 0 | 6 |
| | | | – | 9 | 8 |
| | | | | | 8 |
STEP 15: SUBTRACT 106 - 98 = 8
|
| | | 0 | 2 | 9 | 7 |
| 1 | 4 | 4 | 1 | 6 | 6 |
| | – | 0 | | | |
| | | 4 | 1 | | |
| | – | 2 | 8 | | |
| | | 1 | 3 | 6 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 0 | 6 |
| | | | – | 9 | 8 |
| | | | | | 8 |
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