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What is the quotient and remainder when $ 3584 $ is divided by $ 14 $ ?
Answer
The quotient is 256 and the remainder is 0.
Explanation
Division Table
|
| | 0 | 2 | 5 | 6 |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | – | 7 | 0 | |
| | | | 8 | 4 |
| | | – | 8 | 4 |
| | | | | 0 |
STEP 0: set up a division table
|
| | | | | |
1 | 4 | 3 | 5 | 8 | 4 |
STEP 1: DIVIDE 3 : 14 = 0 with a remainder of 3
|
| | 0 | | | |
1 | 4 | 3 | 5 | 8 | 4 |
STEP 2: MULTIPLY 0 · 14 = 0
|
| | 0 | | | |
1 | 4 | 3 | 5 | 8 | 4 |
| | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | 0 | | | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
STEP 5: DIVIDE 35 : 14 = 2 with a remainder of 7
|
| | 0 | 2 | | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
STEP 6: MULTIPLY 2 · 14 = 28
|
| | 0 | 2 | | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| | 2 | 8 | | |
STEP 7: SUBTRACT 35 - 28 = 7
|
| | 0 | 2 | | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | | |
STEP 8: BRING DOWN
|
| | 0 | 2 | | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
STEP 9: DIVIDE 78 : 14 = 5 with a remainder of 8
|
| | 0 | 2 | 5 | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
STEP 10: MULTIPLY 5 · 14 = 70
|
| | 0 | 2 | 5 | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | | 7 | 0 | |
STEP 11: SUBTRACT 78 - 70 = 8
|
| | 0 | 2 | 5 | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | – | 7 | 0 | |
| | | | 8 | |
STEP 12: BRING DOWN
|
| | 0 | 2 | 5 | |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | – | 7 | 0 | |
| | | | 8 | 4 |
STEP 13: DIVIDE 84 : 14 = 6 with a remainder of 0
|
| | 0 | 2 | 5 | 6 |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | – | 7 | 0 | |
| | | | 8 | 4 |
STEP 14: MULTIPLY 6 · 14 = 84
|
| | 0 | 2 | 5 | 6 |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | – | 7 | 0 | |
| | | | 8 | 4 |
| | | | 8 | 4 |
STEP 15: SUBTRACT 84 - 84 = 0
|
| | 0 | 2 | 5 | 6 |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | – | 7 | 0 | |
| | | | 8 | 4 |
| | | – | 8 | 4 |
| | | | | 0 |
STEP 15: SUBTRACT 84 - 84 = 0
|
| | 0 | 2 | 5 | 6 |
1 | 4 | 3 | 5 | 8 | 4 |
| – | 0 | | | |
| | 3 | 5 | | |
| – | 2 | 8 | | |
| | | 7 | 8 | |
| | – | 7 | 0 | |
| | | | 8 | 4 |
| | | – | 8 | 4 |
| | | | | 0 |
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