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Question
What is the quotient and remainder when $ 7023 $ is divided by $ 17 $ ?
Answer
The quotient is 413 and the remainder is 2.
Explanation
|
Division Table
|
| | | 0 | 4 | 1 | 3 |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | – | 1 | 7 | |
| | | | | 5 | 3 |
| | | | – | 5 | 1 |
| | | | | | 2 |
STEP 0: set up a division table
|
| | | | | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
STEP 1: DIVIDE 7 : 17 = 0 with a remainder of 7
|
| | | 0 | | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
STEP 2: MULTIPLY 0 · 17 = 0
|
| | | 0 | | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | | 0 | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | | 0 | | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
STEP 5: DIVIDE 70 : 17 = 4 with a remainder of 2
|
| | | 0 | 4 | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
STEP 6: MULTIPLY 4 · 17 = 68
|
| | | 0 | 4 | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | | 6 | 8 | | |
STEP 7: SUBTRACT 70 - 68 = 2
|
| | | 0 | 4 | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 4 | | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
STEP 9: DIVIDE 22 : 17 = 1 with a remainder of 5
|
| | | 0 | 4 | 1 | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
STEP 10: MULTIPLY 1 · 17 = 17
|
| | | 0 | 4 | 1 | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | | 1 | 7 | |
STEP 11: SUBTRACT 22 - 17 = 5
|
| | | 0 | 4 | 1 | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | – | 1 | 7 | |
| | | | | 5 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 4 | 1 | |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | – | 1 | 7 | |
| | | | | 5 | 3 |
STEP 13: DIVIDE 53 : 17 = 3 with a remainder of 2
|
| | | 0 | 4 | 1 | 3 |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | – | 1 | 7 | |
| | | | | 5 | 3 |
STEP 14: MULTIPLY 3 · 17 = 51
|
| | | 0 | 4 | 1 | 3 |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | – | 1 | 7 | |
| | | | | 5 | 3 |
| | | | | 5 | 1 |
STEP 15: SUBTRACT 53 - 51 = 2
|
| | | 0 | 4 | 1 | 3 |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | – | 1 | 7 | |
| | | | | 5 | 3 |
| | | | – | 5 | 1 |
| | | | | | 2 |
STEP 15: SUBTRACT 53 - 51 = 2
|
| | | 0 | 4 | 1 | 3 |
| 1 | 7 | 7 | 0 | 2 | 3 |
| | – | 0 | | | |
| | | 7 | 0 | | |
| | – | 6 | 8 | | |
| | | | 2 | 2 | |
| | | – | 1 | 7 | |
| | | | | 5 | 3 |
| | | | – | 5 | 1 |
| | | | | | 2 |
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