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Question
What is the quotient and remainder when $ 6741 $ is divided by $ 43 $ ?
Answer
The quotient is 156 and the remainder is 33.
Explanation
|
Division Table
|
| | | 0 | 1 | 5 | 6 |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | – | 2 | 1 | 5 | |
| | | | 2 | 9 | 1 |
| | | – | 2 | 5 | 8 |
| | | | | 3 | 3 |
STEP 0: set up a division table
|
| | | | | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
STEP 1: DIVIDE 6 : 43 = 0 with a remainder of 6
|
| | | 0 | | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
STEP 2: MULTIPLY 0 · 43 = 0
|
| | | 0 | | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | | 0 | | | |
STEP 3: SUBTRACT 6 - 0 = 6
|
| | | 0 | | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
STEP 5: DIVIDE 67 : 43 = 1 with a remainder of 24
|
| | | 0 | 1 | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
STEP 6: MULTIPLY 1 · 43 = 43
|
| | | 0 | 1 | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | | 4 | 3 | | |
STEP 7: SUBTRACT 67 - 43 = 24
|
| | | 0 | 1 | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
STEP 9: DIVIDE 244 : 43 = 5 with a remainder of 29
|
| | | 0 | 1 | 5 | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
STEP 10: MULTIPLY 5 · 43 = 215
|
| | | 0 | 1 | 5 | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | | 2 | 1 | 5 | |
STEP 11: SUBTRACT 244 - 215 = 29
|
| | | 0 | 1 | 5 | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | – | 2 | 1 | 5 | |
| | | | 2 | 9 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 5 | |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | – | 2 | 1 | 5 | |
| | | | 2 | 9 | 1 |
STEP 13: DIVIDE 291 : 43 = 6 with a remainder of 33
|
| | | 0 | 1 | 5 | 6 |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | – | 2 | 1 | 5 | |
| | | | 2 | 9 | 1 |
STEP 14: MULTIPLY 6 · 43 = 258
|
| | | 0 | 1 | 5 | 6 |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | – | 2 | 1 | 5 | |
| | | | 2 | 9 | 1 |
| | | | 2 | 5 | 8 |
STEP 15: SUBTRACT 291 - 258 = 33
|
| | | 0 | 1 | 5 | 6 |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | – | 2 | 1 | 5 | |
| | | | 2 | 9 | 1 |
| | | – | 2 | 5 | 8 |
| | | | | 3 | 3 |
STEP 15: SUBTRACT 291 - 258 = 33
|
| | | 0 | 1 | 5 | 6 |
| 4 | 3 | 6 | 7 | 4 | 1 |
| | – | 0 | | | |
| | | 6 | 7 | | |
| | – | 4 | 3 | | |
| | | 2 | 4 | 4 | |
| | – | 2 | 1 | 5 | |
| | | | 2 | 9 | 1 |
| | | – | 2 | 5 | 8 |
| | | | | 3 | 3 |
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