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Question
What is the quotient and remainder when $ 8357 $ is divided by $ 7 $ ?
Answer
The quotient is 1193 and the remainder is 6.
Explanation
|
Division Table
|
| | 1 | 1 | 9 | 3 |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | – | 6 | 3 | |
| | | | 2 | 7 |
| | | – | 2 | 1 |
| | | | | 6 |
STEP 0: set up a division table
|
| | | | | |
| 7 | 8 | 3 | 5 | 7 |
STEP 1: DIVIDE 8 : 7 = 1 with a remainder of 1
|
| | 1 | | | |
| 7 | 8 | 3 | 5 | 7 |
STEP 2: MULTIPLY 1 · 7 = 7
|
| | 1 | | | |
| 7 | 8 | 3 | 5 | 7 |
| | 7 | | | |
STEP 3: SUBTRACT 8 - 7 = 1
|
| | 1 | | | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | | | |
|
STEP 4: BRING DOWN
|
| | 1 | | | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
STEP 5: DIVIDE 13 : 7 = 1 with a remainder of 6
|
| | 1 | 1 | | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
STEP 6: MULTIPLY 1 · 7 = 7
|
| | 1 | 1 | | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | | 7 | | |
STEP 7: SUBTRACT 13 - 7 = 6
|
| | 1 | 1 | | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | | |
|
STEP 8: BRING DOWN
|
| | 1 | 1 | | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
STEP 9: DIVIDE 65 : 7 = 9 with a remainder of 2
|
| | 1 | 1 | 9 | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
STEP 10: MULTIPLY 9 · 7 = 63
|
| | 1 | 1 | 9 | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | | 6 | 3 | |
STEP 11: SUBTRACT 65 - 63 = 2
|
| | 1 | 1 | 9 | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | – | 6 | 3 | |
| | | | 2 | |
|
STEP 12: BRING DOWN
|
| | 1 | 1 | 9 | |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | – | 6 | 3 | |
| | | | 2 | 7 |
STEP 13: DIVIDE 27 : 7 = 3 with a remainder of 6
|
| | 1 | 1 | 9 | 3 |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | – | 6 | 3 | |
| | | | 2 | 7 |
STEP 14: MULTIPLY 3 · 7 = 21
|
| | 1 | 1 | 9 | 3 |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | – | 6 | 3 | |
| | | | 2 | 7 |
| | | | 2 | 1 |
STEP 15: SUBTRACT 27 - 21 = 6
|
| | 1 | 1 | 9 | 3 |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | – | 6 | 3 | |
| | | | 2 | 7 |
| | | – | 2 | 1 |
| | | | | 6 |
STEP 15: SUBTRACT 27 - 21 = 6
|
| | 1 | 1 | 9 | 3 |
| 7 | 8 | 3 | 5 | 7 |
| – | 7 | | | |
| | 1 | 3 | | |
| | – | 7 | | |
| | | 6 | 5 | |
| | – | 6 | 3 | |
| | | | 2 | 7 |
| | | – | 2 | 1 |
| | | | | 6 |
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