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Question
What is the quotient and remainder when $ 1000 $ is divided by $ 6 $ ?
Answer
The quotient is 166 and the remainder is 4.
Explanation
|
Division Table
|
| | 0 | 1 | 6 | 6 |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | – | 3 | 6 | |
| | | | 4 | 0 |
| | | – | 3 | 6 |
| | | | | 4 |
STEP 0: set up a division table
|
| | | | | |
| 6 | 1 | 0 | 0 | 0 |
STEP 1: DIVIDE 1 : 6 = 0 with a remainder of 1
|
| | 0 | | | |
| 6 | 1 | 0 | 0 | 0 |
STEP 2: MULTIPLY 0 · 6 = 0
|
| | 0 | | | |
| 6 | 1 | 0 | 0 | 0 |
| | 0 | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | 0 | | | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | | | |
|
STEP 4: BRING DOWN
|
| | 0 | | | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
STEP 5: DIVIDE 10 : 6 = 1 with a remainder of 4
|
| | 0 | 1 | | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
STEP 6: MULTIPLY 1 · 6 = 6
|
| | 0 | 1 | | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | | 6 | | |
STEP 7: SUBTRACT 10 - 6 = 4
|
| | 0 | 1 | | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | | |
|
STEP 8: BRING DOWN
|
| | 0 | 1 | | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
STEP 9: DIVIDE 40 : 6 = 6 with a remainder of 4
|
| | 0 | 1 | 6 | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
STEP 10: MULTIPLY 6 · 6 = 36
|
| | 0 | 1 | 6 | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | | 3 | 6 | |
STEP 11: SUBTRACT 40 - 36 = 4
|
| | 0 | 1 | 6 | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | – | 3 | 6 | |
| | | | 4 | |
|
STEP 12: BRING DOWN
|
| | 0 | 1 | 6 | |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | – | 3 | 6 | |
| | | | 4 | 0 |
STEP 13: DIVIDE 40 : 6 = 6 with a remainder of 4
|
| | 0 | 1 | 6 | 6 |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | – | 3 | 6 | |
| | | | 4 | 0 |
STEP 14: MULTIPLY 6 · 6 = 36
|
| | 0 | 1 | 6 | 6 |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | – | 3 | 6 | |
| | | | 4 | 0 |
| | | | 3 | 6 |
STEP 15: SUBTRACT 40 - 36 = 4
|
| | 0 | 1 | 6 | 6 |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | – | 3 | 6 | |
| | | | 4 | 0 |
| | | – | 3 | 6 |
| | | | | 4 |
STEP 15: SUBTRACT 40 - 36 = 4
|
| | 0 | 1 | 6 | 6 |
| 6 | 1 | 0 | 0 | 0 |
| – | 0 | | | |
| | 1 | 0 | | |
| | – | 6 | | |
| | | 4 | 0 | |
| | – | 3 | 6 | |
| | | | 4 | 0 |
| | | – | 3 | 6 |
| | | | | 4 |
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