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Question
What is the quotient and remainder when $ 7821163 $ is divided by $ 7 $ ?
Answer
The quotient is 1117309 and the remainder is 0.
Explanation
|
Division Table
|
| | 1 | 1 | 1 | 7 | 3 | 0 | 9 |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | – | 0 | | | |
| | | | | 6 | 3 | | |
| | | | – | 6 | 3 | | |
| | | | | | 0 | | |
STEP 0: set up a division table
|
| | | | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
STEP 1: DIVIDE 7 : 7 = 1 with a remainder of 0
|
| | 1 | | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
STEP 2: MULTIPLY 1 · 7 = 7
|
| | 1 | | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| | 7 | | | | | | |
STEP 3: SUBTRACT 7 - 7 = 0
|
| | 1 | | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 0 | | | | | | |
|
STEP 4: BRING DOWN
|
| | 1 | | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
STEP 5: DIVIDE 8 : 7 = 1 with a remainder of 1
|
| | 1 | 1 | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
STEP 6: MULTIPLY 1 · 7 = 7
|
| | 1 | 1 | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| | 7 | | | | | | |
STEP 7: SUBTRACT 8 - 7 = 1
|
| | 1 | 1 | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | | | | | | |
|
STEP 8: BRING DOWN
|
| | 1 | 1 | | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
STEP 9: DIVIDE 12 : 7 = 1 with a remainder of 5
|
| | 1 | 1 | 1 | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
STEP 10: MULTIPLY 1 · 7 = 7
|
| | 1 | 1 | 1 | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | | 7 | | | | | |
STEP 11: SUBTRACT 12 - 7 = 5
|
| | 1 | 1 | 1 | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | | | | | |
|
STEP 12: BRING DOWN
|
| | 1 | 1 | 1 | | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
STEP 13: DIVIDE 51 : 7 = 7 with a remainder of 2
|
| | 1 | 1 | 1 | 7 | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
STEP 14: MULTIPLY 7 · 7 = 49
|
| | 1 | 1 | 1 | 7 | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | | 4 | 9 | | | | |
STEP 15: SUBTRACT 51 - 49 = 2
|
| | 1 | 1 | 1 | 7 | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | | | | |
|
STEP 16: BRING DOWN
|
| | 1 | 1 | 1 | 7 | | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
STEP 17: DIVIDE 21 : 7 = 3 with a remainder of 0
|
| | 1 | 1 | 1 | 7 | 3 | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
STEP 18: MULTIPLY 3 · 7 = 21
|
| | 1 | 1 | 1 | 7 | 3 | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | | 2 | 1 | | | |
STEP 19: SUBTRACT 21 - 21 = 0
|
| | 1 | 1 | 1 | 7 | 3 | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 0 | | | |
|
STEP 20: BRING DOWN
|
| | 1 | 1 | 1 | 7 | 3 | | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
STEP 21: DIVIDE 6 : 7 = 0 with a remainder of 6
|
| | 1 | 1 | 1 | 7 | 3 | 0 | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
STEP 22: MULTIPLY 0 · 7 = 0
|
| | 1 | 1 | 1 | 7 | 3 | 0 | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | | 0 | | | |
STEP 23: SUBTRACT 6 - 0 = 6
|
| | 1 | 1 | 1 | 7 | 3 | 0 | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | – | 0 | | | |
| | | | | 6 | | | |
|
STEP 24: BRING DOWN
|
| | 1 | 1 | 1 | 7 | 3 | 0 | |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | – | 0 | | | |
| | | | | 6 | 3 | | |
STEP 25: DIVIDE 63 : 7 = 9 with a remainder of 0
|
| | 1 | 1 | 1 | 7 | 3 | 0 | 9 |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | – | 0 | | | |
| | | | | 6 | 3 | | |
STEP 26: MULTIPLY 9 · 7 = 63
|
| | 1 | 1 | 1 | 7 | 3 | 0 | 9 |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | – | 0 | | | |
| | | | | 6 | 3 | | |
| | | | | 6 | 3 | | |
STEP 27: SUBTRACT 63 - 63 = 0
|
| | 1 | 1 | 1 | 7 | 3 | 0 | 9 |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | – | 0 | | | |
| | | | | 6 | 3 | | |
| | | | – | 6 | 3 | | |
| | | | | | 0 | | |
STEP 27: SUBTRACT 63 - 63 = 0
|
| | 1 | 1 | 1 | 7 | 3 | 0 | 9 |
| 7 | 7 | 8 | 2 | 1 | 1 | 6 | 3 |
| – | 7 | | | | | | |
| | 8 | | | | | | |
| – | 7 | | | | | | |
| | 1 | 2 | | | | | |
| | – | 7 | | | | | |
| | | 5 | 1 | | | | |
| | – | 4 | 9 | | | | |
| | | | 2 | 1 | | | |
| | | – | 2 | 1 | | | |
| | | | | 6 | | | |
| | | | – | 0 | | | |
| | | | | 6 | 3 | | |
| | | | – | 6 | 3 | | |
| | | | | | 0 | | |
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