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What is the quotient and remainder when $ 2257 $ is divided by $ 11 $ ?
Answer
The quotient is 205 and the remainder is 2.
Explanation
Division Table
|
| | 0 | 2 | 0 | 5 |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | – | 0 | | |
| | | 5 | 7 | |
| | – | 5 | 5 | |
| | | | 2 | |
STEP 0: set up a division table
|
| | | | | |
1 | 1 | 2 | 2 | 5 | 7 |
STEP 1: DIVIDE 2 : 11 = 0 with a remainder of 2
|
| | 0 | | | |
1 | 1 | 2 | 2 | 5 | 7 |
STEP 2: MULTIPLY 0 · 11 = 0
|
| | 0 | | | |
1 | 1 | 2 | 2 | 5 | 7 |
| | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | 0 | | | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
STEP 5: DIVIDE 22 : 11 = 2 with a remainder of 0
|
| | 0 | 2 | | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
STEP 6: MULTIPLY 2 · 11 = 22
|
| | 0 | 2 | | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| | 2 | 2 | | |
STEP 7: SUBTRACT 22 - 22 = 0
|
| | 0 | 2 | | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 0 | | |
STEP 8: BRING DOWN
|
| | 0 | 2 | | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
STEP 9: DIVIDE 5 : 11 = 0 with a remainder of 5
|
| | 0 | 2 | 0 | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
STEP 10: MULTIPLY 0 · 11 = 0
|
| | 0 | 2 | 0 | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | | 0 | | |
STEP 11: SUBTRACT 5 - 0 = 5
|
| | 0 | 2 | 0 | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | – | 0 | | |
| | | 5 | | |
STEP 12: BRING DOWN
|
| | 0 | 2 | 0 | |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | – | 0 | | |
| | | 5 | 7 | |
STEP 13: DIVIDE 57 : 11 = 5 with a remainder of 2
|
| | 0 | 2 | 0 | 5 |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | – | 0 | | |
| | | 5 | 7 | |
STEP 14: MULTIPLY 5 · 11 = 55
|
| | 0 | 2 | 0 | 5 |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | – | 0 | | |
| | | 5 | 7 | |
| | | 5 | 5 | |
STEP 15: SUBTRACT 57 - 55 = 2
|
| | 0 | 2 | 0 | 5 |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | – | 0 | | |
| | | 5 | 7 | |
| | – | 5 | 5 | |
| | | | 2 | |
STEP 15: SUBTRACT 57 - 55 = 2
|
| | 0 | 2 | 0 | 5 |
1 | 1 | 2 | 2 | 5 | 7 |
| – | 0 | | | |
| | 2 | 2 | | |
| – | 2 | 2 | | |
| | | 5 | | |
| | – | 0 | | |
| | | 5 | 7 | |
| | – | 5 | 5 | |
| | | | 2 | |
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