Question
What is the quotient and remainder when $ 11305 $ is divided by $ 17 $ ?
Answer
The quotient is 665 and the remainder is 0.
Explanation
| Division Table | ||||||
| 0 | 0 | 6 | 6 | 5 | ||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| – | 1 | 0 | 2 | |||
| 8 | 5 | |||||
| – | 8 | 5 | ||||
| 0 | ||||||
|
STEP 0: set up a division table |
||||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
|
STEP 1: DIVIDE 1 : 17 = 0 with a remainder of 1 |
||||||
| 0 | ||||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
|
STEP 2: MULTIPLY 0 · 17 = 0 |
||||||
| 0 | ||||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| 0 | ||||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
||||||
| 0 | ||||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | ||||||
| STEP 4: BRING DOWN | ||||||
| 0 | ||||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
|
STEP 5: DIVIDE 11 : 17 = 0 with a remainder of 11 |
||||||
| 0 | 0 | |||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
|
STEP 6: MULTIPLY 0 · 17 = 0 |
||||||
| 0 | 0 | |||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| 0 | ||||||
|
STEP 7: SUBTRACT 11 - 0 = 11 |
||||||
| 0 | 0 | |||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | |||||
| STEP 8: BRING DOWN | ||||||
| 0 | 0 | |||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
|
STEP 9: DIVIDE 113 : 17 = 6 with a remainder of 11 |
||||||
| 0 | 0 | 6 | ||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
|
STEP 10: MULTIPLY 6 · 17 = 102 |
||||||
| 0 | 0 | 6 | ||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| 1 | 0 | 2 | ||||
|
STEP 11: SUBTRACT 113 - 102 = 11 |
||||||
| 0 | 0 | 6 | ||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | |||||
| STEP 12: BRING DOWN | ||||||
| 0 | 0 | 6 | ||||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
|
STEP 13: DIVIDE 110 : 17 = 6 with a remainder of 8 |
||||||
| 0 | 0 | 6 | 6 | |||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
|
STEP 14: MULTIPLY 6 · 17 = 102 |
||||||
| 0 | 0 | 6 | 6 | |||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| 1 | 0 | 2 | ||||
|
STEP 15: SUBTRACT 110 - 102 = 8 |
||||||
| 0 | 0 | 6 | 6 | |||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| – | 1 | 0 | 2 | |||
| 8 | ||||||
| STEP 16: BRING DOWN | ||||||
| 0 | 0 | 6 | 6 | |||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| – | 1 | 0 | 2 | |||
| 8 | 5 | |||||
|
STEP 17: DIVIDE 85 : 17 = 5 with a remainder of 0 |
||||||
| 0 | 0 | 6 | 6 | 5 | ||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| – | 1 | 0 | 2 | |||
| 8 | 5 | |||||
|
STEP 18: MULTIPLY 5 · 17 = 85 |
||||||
| 0 | 0 | 6 | 6 | 5 | ||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| – | 1 | 0 | 2 | |||
| 8 | 5 | |||||
| 8 | 5 | |||||
|
STEP 19: SUBTRACT 85 - 85 = 0 |
||||||
| 0 | 0 | 6 | 6 | 5 | ||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| – | 1 | 0 | 2 | |||
| 8 | 5 | |||||
| – | 8 | 5 | ||||
| 0 | ||||||
|
STEP 19: SUBTRACT 85 - 85 = 0 |
||||||
| 0 | 0 | 6 | 6 | 5 | ||
| 1 | 7 | 1 | 1 | 3 | 0 | 5 |
| – | 0 | |||||
| 1 | 1 | |||||
| – | 0 | |||||
| 1 | 1 | 3 | ||||
| – | 1 | 0 | 2 | |||
| 1 | 1 | 0 | ||||
| – | 1 | 0 | 2 | |||
| 8 | 5 | |||||
| – | 8 | 5 | ||||
| 0 | ||||||
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