Question
What is the quotient and remainder when $ 1005 $ is divided by $ 67 $ ?
Answer
The quotient is 15 and the remainder is 0.
Explanation
| Division Table | |||||
| 0 | 0 | 1 | 5 | ||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| – | 6 | 7 | |||
| 3 | 3 | 5 | |||
| – | 3 | 3 | 5 | ||
| 0 | |||||
|
STEP 0: set up a division table |
|||||
| 6 | 7 | 1 | 0 | 0 | 5 |
|
STEP 1: DIVIDE 1 : 67 = 0 with a remainder of 1 |
|||||
| 0 | |||||
| 6 | 7 | 1 | 0 | 0 | 5 |
|
STEP 2: MULTIPLY 0 · 67 = 0 |
|||||
| 0 | |||||
| 6 | 7 | 1 | 0 | 0 | 5 |
| 0 | |||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
|||||
| 0 | |||||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | |||||
| STEP 4: BRING DOWN | |||||
| 0 | |||||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
|
STEP 5: DIVIDE 10 : 67 = 0 with a remainder of 10 |
|||||
| 0 | 0 | ||||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
|
STEP 6: MULTIPLY 0 · 67 = 0 |
|||||
| 0 | 0 | ||||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| 0 | |||||
|
STEP 7: SUBTRACT 10 - 0 = 10 |
|||||
| 0 | 0 | ||||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | ||||
| STEP 8: BRING DOWN | |||||
| 0 | 0 | ||||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
|
STEP 9: DIVIDE 100 : 67 = 1 with a remainder of 33 |
|||||
| 0 | 0 | 1 | |||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
|
STEP 10: MULTIPLY 1 · 67 = 67 |
|||||
| 0 | 0 | 1 | |||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| 6 | 7 | ||||
|
STEP 11: SUBTRACT 100 - 67 = 33 |
|||||
| 0 | 0 | 1 | |||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| – | 6 | 7 | |||
| 3 | 3 | ||||
| STEP 12: BRING DOWN | |||||
| 0 | 0 | 1 | |||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| – | 6 | 7 | |||
| 3 | 3 | 5 | |||
|
STEP 13: DIVIDE 335 : 67 = 5 with a remainder of 0 |
|||||
| 0 | 0 | 1 | 5 | ||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| – | 6 | 7 | |||
| 3 | 3 | 5 | |||
|
STEP 14: MULTIPLY 5 · 67 = 335 |
|||||
| 0 | 0 | 1 | 5 | ||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| – | 6 | 7 | |||
| 3 | 3 | 5 | |||
| 3 | 3 | 5 | |||
|
STEP 15: SUBTRACT 335 - 335 = 0 |
|||||
| 0 | 0 | 1 | 5 | ||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| – | 6 | 7 | |||
| 3 | 3 | 5 | |||
| – | 3 | 3 | 5 | ||
| 0 | |||||
|
STEP 15: SUBTRACT 335 - 335 = 0 |
|||||
| 0 | 0 | 1 | 5 | ||
| 6 | 7 | 1 | 0 | 0 | 5 |
| – | 0 | ||||
| 1 | 0 | ||||
| – | 0 | ||||
| 1 | 0 | 0 | |||
| – | 6 | 7 | |||
| 3 | 3 | 5 | |||
| – | 3 | 3 | 5 | ||
| 0 | |||||
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