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What is the quotient and remainder when $ 7146 $ is divided by $ 41 $ ?
Answer
The quotient is 174 and the remainder is 12.
Explanation
Division Table
|
| | 0 | 1 | 7 | 4 |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| – | 2 | 8 | 7 | |
| | | 1 | 7 | 6 |
| | – | 1 | 6 | 4 |
| | | | 1 | 2 |
STEP 0: set up a division table
|
| | | | | |
4 | 1 | 7 | 1 | 4 | 6 |
STEP 1: DIVIDE 7 : 41 = 0 with a remainder of 7
|
| | 0 | | | |
4 | 1 | 7 | 1 | 4 | 6 |
STEP 2: MULTIPLY 0 · 41 = 0
|
| | 0 | | | |
4 | 1 | 7 | 1 | 4 | 6 |
| | 0 | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | 0 | | | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
STEP 5: DIVIDE 71 : 41 = 1 with a remainder of 30
|
| | 0 | 1 | | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
STEP 6: MULTIPLY 1 · 41 = 41
|
| | 0 | 1 | | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| | 4 | 1 | | |
STEP 7: SUBTRACT 71 - 41 = 30
|
| | 0 | 1 | | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | | |
STEP 8: BRING DOWN
|
| | 0 | 1 | | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
STEP 9: DIVIDE 304 : 41 = 7 with a remainder of 17
|
| | 0 | 1 | 7 | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
STEP 10: MULTIPLY 7 · 41 = 287
|
| | 0 | 1 | 7 | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| | 2 | 8 | 7 | |
STEP 11: SUBTRACT 304 - 287 = 17
|
| | 0 | 1 | 7 | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| – | 2 | 8 | 7 | |
| | | 1 | 7 | |
STEP 12: BRING DOWN
|
| | 0 | 1 | 7 | |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| – | 2 | 8 | 7 | |
| | | 1 | 7 | 6 |
STEP 13: DIVIDE 176 : 41 = 4 with a remainder of 12
|
| | 0 | 1 | 7 | 4 |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| – | 2 | 8 | 7 | |
| | | 1 | 7 | 6 |
STEP 14: MULTIPLY 4 · 41 = 164
|
| | 0 | 1 | 7 | 4 |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| – | 2 | 8 | 7 | |
| | | 1 | 7 | 6 |
| | | 1 | 6 | 4 |
STEP 15: SUBTRACT 176 - 164 = 12
|
| | 0 | 1 | 7 | 4 |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| – | 2 | 8 | 7 | |
| | | 1 | 7 | 6 |
| | – | 1 | 6 | 4 |
| | | | 1 | 2 |
STEP 15: SUBTRACT 176 - 164 = 12
|
| | 0 | 1 | 7 | 4 |
4 | 1 | 7 | 1 | 4 | 6 |
| – | 0 | | | |
| | 7 | 1 | | |
| – | 4 | 1 | | |
| | 3 | 0 | 4 | |
| – | 2 | 8 | 7 | |
| | | 1 | 7 | 6 |
| | – | 1 | 6 | 4 |
| | | | 1 | 2 |
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