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Question
What is the quotient and remainder when $ 2914 $ is divided by $ 27 $ ?
Answer
The quotient is 107 and the remainder is 25.
Explanation
|
Division Table
|
| | | 0 | 1 | 0 | 7 |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | – | 0 | |
| | | | 2 | 1 | 4 |
| | | – | 1 | 8 | 9 |
| | | | | 2 | 5 |
STEP 0: set up a division table
|
| | | | | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
STEP 1: DIVIDE 2 : 27 = 0 with a remainder of 2
|
| | | 0 | | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
STEP 2: MULTIPLY 0 · 27 = 0
|
| | | 0 | | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
STEP 5: DIVIDE 29 : 27 = 1 with a remainder of 2
|
| | | 0 | 1 | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
STEP 6: MULTIPLY 1 · 27 = 27
|
| | | 0 | 1 | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | | 2 | 7 | | |
STEP 7: SUBTRACT 29 - 27 = 2
|
| | | 0 | 1 | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
STEP 9: DIVIDE 21 : 27 = 0 with a remainder of 21
|
| | | 0 | 1 | 0 | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
STEP 10: MULTIPLY 0 · 27 = 0
|
| | | 0 | 1 | 0 | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | | 0 | |
STEP 11: SUBTRACT 21 - 0 = 21
|
| | | 0 | 1 | 0 | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | – | 0 | |
| | | | 2 | 1 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 0 | |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | – | 0 | |
| | | | 2 | 1 | 4 |
STEP 13: DIVIDE 214 : 27 = 7 with a remainder of 25
|
| | | 0 | 1 | 0 | 7 |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | – | 0 | |
| | | | 2 | 1 | 4 |
STEP 14: MULTIPLY 7 · 27 = 189
|
| | | 0 | 1 | 0 | 7 |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | – | 0 | |
| | | | 2 | 1 | 4 |
| | | | 1 | 8 | 9 |
STEP 15: SUBTRACT 214 - 189 = 25
|
| | | 0 | 1 | 0 | 7 |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | – | 0 | |
| | | | 2 | 1 | 4 |
| | | – | 1 | 8 | 9 |
| | | | | 2 | 5 |
STEP 15: SUBTRACT 214 - 189 = 25
|
| | | 0 | 1 | 0 | 7 |
| 2 | 7 | 2 | 9 | 1 | 4 |
| | – | 0 | | | |
| | | 2 | 9 | | |
| | – | 2 | 7 | | |
| | | | 2 | 1 | |
| | | | – | 0 | |
| | | | 2 | 1 | 4 |
| | | – | 1 | 8 | 9 |
| | | | | 2 | 5 |
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