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What is the quotient and remainder when $ 7865 $ is divided by $ 17 $ ?
Answer
The quotient is 462 and the remainder is 11.
Explanation
Division Table
|
| | 0 | 4 | 6 | 2 |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| – | 1 | 0 | 2 | |
| | | | 4 | 5 |
| | | – | 3 | 4 |
| | | | 1 | 1 |
STEP 0: set up a division table
|
| | | | | |
1 | 7 | 7 | 8 | 6 | 5 |
STEP 1: DIVIDE 7 : 17 = 0 with a remainder of 7
|
| | 0 | | | |
1 | 7 | 7 | 8 | 6 | 5 |
STEP 2: MULTIPLY 0 · 17 = 0
|
| | 0 | | | |
1 | 7 | 7 | 8 | 6 | 5 |
| | 0 | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | 0 | | | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
STEP 5: DIVIDE 78 : 17 = 4 with a remainder of 10
|
| | 0 | 4 | | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
STEP 6: MULTIPLY 4 · 17 = 68
|
| | 0 | 4 | | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| | 6 | 8 | | |
STEP 7: SUBTRACT 78 - 68 = 10
|
| | 0 | 4 | | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | | |
STEP 8: BRING DOWN
|
| | 0 | 4 | | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
STEP 9: DIVIDE 106 : 17 = 6 with a remainder of 4
|
| | 0 | 4 | 6 | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
STEP 10: MULTIPLY 6 · 17 = 102
|
| | 0 | 4 | 6 | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| | 1 | 0 | 2 | |
STEP 11: SUBTRACT 106 - 102 = 4
|
| | 0 | 4 | 6 | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| – | 1 | 0 | 2 | |
| | | | 4 | |
STEP 12: BRING DOWN
|
| | 0 | 4 | 6 | |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| – | 1 | 0 | 2 | |
| | | | 4 | 5 |
STEP 13: DIVIDE 45 : 17 = 2 with a remainder of 11
|
| | 0 | 4 | 6 | 2 |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| – | 1 | 0 | 2 | |
| | | | 4 | 5 |
STEP 14: MULTIPLY 2 · 17 = 34
|
| | 0 | 4 | 6 | 2 |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| – | 1 | 0 | 2 | |
| | | | 4 | 5 |
| | | | 3 | 4 |
STEP 15: SUBTRACT 45 - 34 = 11
|
| | 0 | 4 | 6 | 2 |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| – | 1 | 0 | 2 | |
| | | | 4 | 5 |
| | | – | 3 | 4 |
| | | | 1 | 1 |
STEP 15: SUBTRACT 45 - 34 = 11
|
| | 0 | 4 | 6 | 2 |
1 | 7 | 7 | 8 | 6 | 5 |
| – | 0 | | | |
| | 7 | 8 | | |
| – | 6 | 8 | | |
| | 1 | 0 | 6 | |
| – | 1 | 0 | 2 | |
| | | | 4 | 5 |
| | | – | 3 | 4 |
| | | | 1 | 1 |
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