Question
What is the quotient and remainder when $ 1331 $ is divided by $ 11 $ ?
Answer
The quotient is 121 and the remainder is 0.
Explanation
| Division Table | |||||
| 0 | 1 | 2 | 1 | ||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| – | 2 | 2 | |||
| 1 | 1 | ||||
| – | 1 | 1 | |||
| 0 | |||||
|
STEP 0: set up a division table |
|||||
| 1 | 1 | 1 | 3 | 3 | 1 |
|
STEP 1: DIVIDE 1 : 11 = 0 with a remainder of 1 |
|||||
| 0 | |||||
| 1 | 1 | 1 | 3 | 3 | 1 |
|
STEP 2: MULTIPLY 0 · 11 = 0 |
|||||
| 0 | |||||
| 1 | 1 | 1 | 3 | 3 | 1 |
| 0 | |||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
|||||
| 0 | |||||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | |||||
| STEP 4: BRING DOWN | |||||
| 0 | |||||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
|
STEP 5: DIVIDE 13 : 11 = 1 with a remainder of 2 |
|||||
| 0 | 1 | ||||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
|
STEP 6: MULTIPLY 1 · 11 = 11 |
|||||
| 0 | 1 | ||||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| 1 | 1 | ||||
|
STEP 7: SUBTRACT 13 - 11 = 2 |
|||||
| 0 | 1 | ||||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | |||||
| STEP 8: BRING DOWN | |||||
| 0 | 1 | ||||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
|
STEP 9: DIVIDE 23 : 11 = 2 with a remainder of 1 |
|||||
| 0 | 1 | 2 | |||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
|
STEP 10: MULTIPLY 2 · 11 = 22 |
|||||
| 0 | 1 | 2 | |||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| 2 | 2 | ||||
|
STEP 11: SUBTRACT 23 - 22 = 1 |
|||||
| 0 | 1 | 2 | |||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| – | 2 | 2 | |||
| 1 | |||||
| STEP 12: BRING DOWN | |||||
| 0 | 1 | 2 | |||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| – | 2 | 2 | |||
| 1 | 1 | ||||
|
STEP 13: DIVIDE 11 : 11 = 1 with a remainder of 0 |
|||||
| 0 | 1 | 2 | 1 | ||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| – | 2 | 2 | |||
| 1 | 1 | ||||
|
STEP 14: MULTIPLY 1 · 11 = 11 |
|||||
| 0 | 1 | 2 | 1 | ||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| – | 2 | 2 | |||
| 1 | 1 | ||||
| 1 | 1 | ||||
|
STEP 15: SUBTRACT 11 - 11 = 0 |
|||||
| 0 | 1 | 2 | 1 | ||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| – | 2 | 2 | |||
| 1 | 1 | ||||
| – | 1 | 1 | |||
| 0 | |||||
|
STEP 15: SUBTRACT 11 - 11 = 0 |
|||||
| 0 | 1 | 2 | 1 | ||
| 1 | 1 | 1 | 3 | 3 | 1 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 1 | 1 | |||
| 2 | 3 | ||||
| – | 2 | 2 | |||
| 1 | 1 | ||||
| – | 1 | 1 | |||
| 0 | |||||
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