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What is the quotient and remainder when $ 10536 $ is divided by $ 7 $ ?
Answer
The quotient is 1505 and the remainder is 1.
Explanation
Division Table
|
| 0 | 1 | 5 | 0 | 5 |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | – | 0 | | |
| | | 3 | 6 | |
| | – | 3 | 5 | |
| | | | 1 | |
STEP 0: set up a division table
|
| | | | | |
7 | 1 | 0 | 5 | 3 | 6 |
STEP 1: DIVIDE 1 : 7 = 0 with a remainder of 1
|
| 0 | | | | |
7 | 1 | 0 | 5 | 3 | 6 |
STEP 2: MULTIPLY 0 · 7 = 0
|
| 0 | | | | |
7 | 1 | 0 | 5 | 3 | 6 |
| 0 | | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| 0 | | | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | | | | |
STEP 4: BRING DOWN
|
| 0 | | | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
STEP 5: DIVIDE 10 : 7 = 1 with a remainder of 3
|
| 0 | 1 | | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
STEP 6: MULTIPLY 1 · 7 = 7
|
| 0 | 1 | | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| | 7 | | | |
STEP 7: SUBTRACT 10 - 7 = 3
|
| 0 | 1 | | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | | | |
STEP 8: BRING DOWN
|
| 0 | 1 | | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
STEP 9: DIVIDE 35 : 7 = 5 with a remainder of 0
|
| 0 | 1 | 5 | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
STEP 10: MULTIPLY 5 · 7 = 35
|
| 0 | 1 | 5 | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| | 3 | 5 | | |
STEP 11: SUBTRACT 35 - 35 = 0
|
| 0 | 1 | 5 | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 0 | | |
STEP 12: BRING DOWN
|
| 0 | 1 | 5 | | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
STEP 13: DIVIDE 3 : 7 = 0 with a remainder of 3
|
| 0 | 1 | 5 | 0 | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
STEP 14: MULTIPLY 0 · 7 = 0
|
| 0 | 1 | 5 | 0 | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | | 0 | | |
STEP 15: SUBTRACT 3 - 0 = 3
|
| 0 | 1 | 5 | 0 | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | – | 0 | | |
| | | 3 | | |
STEP 16: BRING DOWN
|
| 0 | 1 | 5 | 0 | |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | – | 0 | | |
| | | 3 | 6 | |
STEP 17: DIVIDE 36 : 7 = 5 with a remainder of 1
|
| 0 | 1 | 5 | 0 | 5 |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | – | 0 | | |
| | | 3 | 6 | |
STEP 18: MULTIPLY 5 · 7 = 35
|
| 0 | 1 | 5 | 0 | 5 |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | – | 0 | | |
| | | 3 | 6 | |
| | | 3 | 5 | |
STEP 19: SUBTRACT 36 - 35 = 1
|
| 0 | 1 | 5 | 0 | 5 |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | – | 0 | | |
| | | 3 | 6 | |
| | – | 3 | 5 | |
| | | | 1 | |
STEP 19: SUBTRACT 36 - 35 = 1
|
| 0 | 1 | 5 | 0 | 5 |
7 | 1 | 0 | 5 | 3 | 6 |
– | 0 | | | | |
| 1 | 0 | | | |
| – | 7 | | | |
| | 3 | 5 | | |
| – | 3 | 5 | | |
| | | 3 | | |
| | – | 0 | | |
| | | 3 | 6 | |
| | – | 3 | 5 | |
| | | | 1 | |
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