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Question
What is the quotient and remainder when $ 3429 $ is divided by $ 27 $ ?
Answer
The quotient is 127 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 1 | 2 | 7 |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | – | 5 | 4 | |
| | | | 1 | 8 | 9 |
| | | – | 1 | 8 | 9 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
STEP 1: DIVIDE 3 : 27 = 0 with a remainder of 3
|
| | | 0 | | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
STEP 2: MULTIPLY 0 · 27 = 0
|
| | | 0 | | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
STEP 5: DIVIDE 34 : 27 = 1 with a remainder of 7
|
| | | 0 | 1 | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
STEP 6: MULTIPLY 1 · 27 = 27
|
| | | 0 | 1 | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | | 2 | 7 | | |
STEP 7: SUBTRACT 34 - 27 = 7
|
| | | 0 | 1 | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
STEP 9: DIVIDE 72 : 27 = 2 with a remainder of 18
|
| | | 0 | 1 | 2 | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
STEP 10: MULTIPLY 2 · 27 = 54
|
| | | 0 | 1 | 2 | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | | 5 | 4 | |
STEP 11: SUBTRACT 72 - 54 = 18
|
| | | 0 | 1 | 2 | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | – | 5 | 4 | |
| | | | 1 | 8 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 2 | |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | – | 5 | 4 | |
| | | | 1 | 8 | 9 |
STEP 13: DIVIDE 189 : 27 = 7 with a remainder of 0
|
| | | 0 | 1 | 2 | 7 |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | – | 5 | 4 | |
| | | | 1 | 8 | 9 |
STEP 14: MULTIPLY 7 · 27 = 189
|
| | | 0 | 1 | 2 | 7 |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | – | 5 | 4 | |
| | | | 1 | 8 | 9 |
| | | | 1 | 8 | 9 |
STEP 15: SUBTRACT 189 - 189 = 0
|
| | | 0 | 1 | 2 | 7 |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | – | 5 | 4 | |
| | | | 1 | 8 | 9 |
| | | – | 1 | 8 | 9 |
| | | | | | 0 |
STEP 15: SUBTRACT 189 - 189 = 0
|
| | | 0 | 1 | 2 | 7 |
| 2 | 7 | 3 | 4 | 2 | 9 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 7 | | |
| | | | 7 | 2 | |
| | | – | 5 | 4 | |
| | | | 1 | 8 | 9 |
| | | – | 1 | 8 | 9 |
| | | | | | 0 |
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