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Question
What is the quotient and remainder when $ 8781 $ is divided by $ 31 $ ?
Answer
The quotient is 283 and the remainder is 8.
Explanation
|
Division Table
|
| | | 0 | 2 | 8 | 3 |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | – | 2 | 4 | 8 | |
| | | | 1 | 0 | 1 |
| | | | – | 9 | 3 |
| | | | | | 8 |
STEP 0: set up a division table
|
| | | | | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
STEP 1: DIVIDE 8 : 31 = 0 with a remainder of 8
|
| | | 0 | | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
STEP 2: MULTIPLY 0 · 31 = 0
|
| | | 0 | | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | | 0 | | | |
STEP 3: SUBTRACT 8 - 0 = 8
|
| | | 0 | | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
STEP 5: DIVIDE 87 : 31 = 2 with a remainder of 25
|
| | | 0 | 2 | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
STEP 6: MULTIPLY 2 · 31 = 62
|
| | | 0 | 2 | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | | 6 | 2 | | |
STEP 7: SUBTRACT 87 - 62 = 25
|
| | | 0 | 2 | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
STEP 9: DIVIDE 258 : 31 = 8 with a remainder of 10
|
| | | 0 | 2 | 8 | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
STEP 10: MULTIPLY 8 · 31 = 248
|
| | | 0 | 2 | 8 | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | | 2 | 4 | 8 | |
STEP 11: SUBTRACT 258 - 248 = 10
|
| | | 0 | 2 | 8 | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | – | 2 | 4 | 8 | |
| | | | 1 | 0 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 8 | |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | – | 2 | 4 | 8 | |
| | | | 1 | 0 | 1 |
STEP 13: DIVIDE 101 : 31 = 3 with a remainder of 8
|
| | | 0 | 2 | 8 | 3 |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | – | 2 | 4 | 8 | |
| | | | 1 | 0 | 1 |
STEP 14: MULTIPLY 3 · 31 = 93
|
| | | 0 | 2 | 8 | 3 |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | – | 2 | 4 | 8 | |
| | | | 1 | 0 | 1 |
| | | | | 9 | 3 |
STEP 15: SUBTRACT 101 - 93 = 8
|
| | | 0 | 2 | 8 | 3 |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | – | 2 | 4 | 8 | |
| | | | 1 | 0 | 1 |
| | | | – | 9 | 3 |
| | | | | | 8 |
STEP 15: SUBTRACT 101 - 93 = 8
|
| | | 0 | 2 | 8 | 3 |
| 3 | 1 | 8 | 7 | 8 | 1 |
| | – | 0 | | | |
| | | 8 | 7 | | |
| | – | 6 | 2 | | |
| | | 2 | 5 | 8 | |
| | – | 2 | 4 | 8 | |
| | | | 1 | 0 | 1 |
| | | | – | 9 | 3 |
| | | | | | 8 |
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