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Question
What is the quotient and remainder when $ 1654 $ is divided by $ 46 $ ?
Answer
The quotient is 35 and the remainder is 44.
Explanation
|
Division Table
|
| | | 0 | 0 | 3 | 5 |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | – | 1 | 3 | 8 | |
| | | | 2 | 7 | 4 |
| | | – | 2 | 3 | 0 |
| | | | | 4 | 4 |
STEP 0: set up a division table
|
| | | | | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
STEP 1: DIVIDE 1 : 46 = 0 with a remainder of 1
|
| | | 0 | | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
STEP 2: MULTIPLY 0 · 46 = 0
|
| | | 0 | | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | | 0 | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | | 0 | | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
STEP 5: DIVIDE 16 : 46 = 0 with a remainder of 16
|
| | | 0 | 0 | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
STEP 6: MULTIPLY 0 · 46 = 0
|
| | | 0 | 0 | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 16 - 0 = 16
|
| | | 0 | 0 | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
STEP 9: DIVIDE 165 : 46 = 3 with a remainder of 27
|
| | | 0 | 0 | 3 | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
STEP 10: MULTIPLY 3 · 46 = 138
|
| | | 0 | 0 | 3 | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | | 1 | 3 | 8 | |
STEP 11: SUBTRACT 165 - 138 = 27
|
| | | 0 | 0 | 3 | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | – | 1 | 3 | 8 | |
| | | | 2 | 7 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 0 | 3 | |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | – | 1 | 3 | 8 | |
| | | | 2 | 7 | 4 |
STEP 13: DIVIDE 274 : 46 = 5 with a remainder of 44
|
| | | 0 | 0 | 3 | 5 |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | – | 1 | 3 | 8 | |
| | | | 2 | 7 | 4 |
STEP 14: MULTIPLY 5 · 46 = 230
|
| | | 0 | 0 | 3 | 5 |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | – | 1 | 3 | 8 | |
| | | | 2 | 7 | 4 |
| | | | 2 | 3 | 0 |
STEP 15: SUBTRACT 274 - 230 = 44
|
| | | 0 | 0 | 3 | 5 |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | – | 1 | 3 | 8 | |
| | | | 2 | 7 | 4 |
| | | – | 2 | 3 | 0 |
| | | | | 4 | 4 |
STEP 15: SUBTRACT 274 - 230 = 44
|
| | | 0 | 0 | 3 | 5 |
| 4 | 6 | 1 | 6 | 5 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 5 | |
| | – | 1 | 3 | 8 | |
| | | | 2 | 7 | 4 |
| | | – | 2 | 3 | 0 |
| | | | | 4 | 4 |
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