Question
What is the quotient and remainder when $ 7123 $ is divided by $ 17 $ ?
Answer
The quotient is 419 and the remainder is 0.
Explanation
| Division Table | |||||
| 0 | 4 | 1 | 9 | ||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| – | 1 | 7 | |||
| 1 | 5 | 3 | |||
| – | 1 | 5 | 3 | ||
| 0 | |||||
|
STEP 0: set up a division table |
|||||
| 1 | 7 | 7 | 1 | 2 | 3 |
|
STEP 1: DIVIDE 7 : 17 = 0 with a remainder of 7 |
|||||
| 0 | |||||
| 1 | 7 | 7 | 1 | 2 | 3 |
|
STEP 2: MULTIPLY 0 · 17 = 0 |
|||||
| 0 | |||||
| 1 | 7 | 7 | 1 | 2 | 3 |
| 0 | |||||
|
STEP 3: SUBTRACT 7 - 0 = 7 |
|||||
| 0 | |||||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | |||||
| STEP 4: BRING DOWN | |||||
| 0 | |||||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
|
STEP 5: DIVIDE 71 : 17 = 4 with a remainder of 3 |
|||||
| 0 | 4 | ||||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
|
STEP 6: MULTIPLY 4 · 17 = 68 |
|||||
| 0 | 4 | ||||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| 6 | 8 | ||||
|
STEP 7: SUBTRACT 71 - 68 = 3 |
|||||
| 0 | 4 | ||||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | |||||
| STEP 8: BRING DOWN | |||||
| 0 | 4 | ||||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
|
STEP 9: DIVIDE 32 : 17 = 1 with a remainder of 15 |
|||||
| 0 | 4 | 1 | |||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
|
STEP 10: MULTIPLY 1 · 17 = 17 |
|||||
| 0 | 4 | 1 | |||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| 1 | 7 | ||||
|
STEP 11: SUBTRACT 32 - 17 = 15 |
|||||
| 0 | 4 | 1 | |||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| – | 1 | 7 | |||
| 1 | 5 | ||||
| STEP 12: BRING DOWN | |||||
| 0 | 4 | 1 | |||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| – | 1 | 7 | |||
| 1 | 5 | 3 | |||
|
STEP 13: DIVIDE 153 : 17 = 9 with a remainder of 0 |
|||||
| 0 | 4 | 1 | 9 | ||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| – | 1 | 7 | |||
| 1 | 5 | 3 | |||
|
STEP 14: MULTIPLY 9 · 17 = 153 |
|||||
| 0 | 4 | 1 | 9 | ||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| – | 1 | 7 | |||
| 1 | 5 | 3 | |||
| 1 | 5 | 3 | |||
|
STEP 15: SUBTRACT 153 - 153 = 0 |
|||||
| 0 | 4 | 1 | 9 | ||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| – | 1 | 7 | |||
| 1 | 5 | 3 | |||
| – | 1 | 5 | 3 | ||
| 0 | |||||
|
STEP 15: SUBTRACT 153 - 153 = 0 |
|||||
| 0 | 4 | 1 | 9 | ||
| 1 | 7 | 7 | 1 | 2 | 3 |
| – | 0 | ||||
| 7 | 1 | ||||
| – | 6 | 8 | |||
| 3 | 2 | ||||
| – | 1 | 7 | |||
| 1 | 5 | 3 | |||
| – | 1 | 5 | 3 | ||
| 0 | |||||
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