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What is the quotient and remainder when $ 3200 $ is divided by $ 27 $ ?
Answer
The quotient is 118 and the remainder is 14.
Explanation
Division Table
|
| | 0 | 1 | 1 | 8 |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | – | 2 | 7 | |
| | | 2 | 3 | 0 |
| | – | 2 | 1 | 6 |
| | | | 1 | 4 |
STEP 0: set up a division table
|
| | | | | |
2 | 7 | 3 | 2 | 0 | 0 |
STEP 1: DIVIDE 3 : 27 = 0 with a remainder of 3
|
| | 0 | | | |
2 | 7 | 3 | 2 | 0 | 0 |
STEP 2: MULTIPLY 0 · 27 = 0
|
| | 0 | | | |
2 | 7 | 3 | 2 | 0 | 0 |
| | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | 0 | | | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
STEP 5: DIVIDE 32 : 27 = 1 with a remainder of 5
|
| | 0 | 1 | | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
STEP 6: MULTIPLY 1 · 27 = 27
|
| | 0 | 1 | | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| | 2 | 7 | | |
STEP 7: SUBTRACT 32 - 27 = 5
|
| | 0 | 1 | | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | | |
STEP 8: BRING DOWN
|
| | 0 | 1 | | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
STEP 9: DIVIDE 50 : 27 = 1 with a remainder of 23
|
| | 0 | 1 | 1 | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
STEP 10: MULTIPLY 1 · 27 = 27
|
| | 0 | 1 | 1 | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | | 2 | 7 | |
STEP 11: SUBTRACT 50 - 27 = 23
|
| | 0 | 1 | 1 | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | – | 2 | 7 | |
| | | 2 | 3 | |
STEP 12: BRING DOWN
|
| | 0 | 1 | 1 | |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | – | 2 | 7 | |
| | | 2 | 3 | 0 |
STEP 13: DIVIDE 230 : 27 = 8 with a remainder of 14
|
| | 0 | 1 | 1 | 8 |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | – | 2 | 7 | |
| | | 2 | 3 | 0 |
STEP 14: MULTIPLY 8 · 27 = 216
|
| | 0 | 1 | 1 | 8 |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | – | 2 | 7 | |
| | | 2 | 3 | 0 |
| | | 2 | 1 | 6 |
STEP 15: SUBTRACT 230 - 216 = 14
|
| | 0 | 1 | 1 | 8 |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | – | 2 | 7 | |
| | | 2 | 3 | 0 |
| | – | 2 | 1 | 6 |
| | | | 1 | 4 |
STEP 15: SUBTRACT 230 - 216 = 14
|
| | 0 | 1 | 1 | 8 |
2 | 7 | 3 | 2 | 0 | 0 |
| – | 0 | | | |
| | 3 | 2 | | |
| – | 2 | 7 | | |
| | | 5 | 0 | |
| | – | 2 | 7 | |
| | | 2 | 3 | 0 |
| | – | 2 | 1 | 6 |
| | | | 1 | 4 |
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