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Question
What is the quotient and remainder when $ 27203 $ is divided by $ 11 $ ?
Answer
The quotient is 2473 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 2 | 4 | 7 | 3 |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | – | 7 | 7 | |
| | | | | | 3 | 3 |
| | | | | – | 3 | 3 |
| | | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
STEP 1: DIVIDE 2 : 11 = 0 with a remainder of 2
|
| | | 0 | | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
STEP 2: MULTIPLY 0 · 11 = 0
|
| | | 0 | | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | | 0 | | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
STEP 5: DIVIDE 27 : 11 = 2 with a remainder of 5
|
| | | 0 | 2 | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
STEP 6: MULTIPLY 2 · 11 = 22
|
| | | 0 | 2 | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | | 2 | 2 | | | |
STEP 7: SUBTRACT 27 - 22 = 5
|
| | | 0 | 2 | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
STEP 9: DIVIDE 52 : 11 = 4 with a remainder of 8
|
| | | 0 | 2 | 4 | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
STEP 10: MULTIPLY 4 · 11 = 44
|
| | | 0 | 2 | 4 | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | | 4 | 4 | | |
STEP 11: SUBTRACT 52 - 44 = 8
|
| | | 0 | 2 | 4 | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 4 | | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
STEP 13: DIVIDE 80 : 11 = 7 with a remainder of 3
|
| | | 0 | 2 | 4 | 7 | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
STEP 14: MULTIPLY 7 · 11 = 77
|
| | | 0 | 2 | 4 | 7 | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | | 7 | 7 | |
STEP 15: SUBTRACT 80 - 77 = 3
|
| | | 0 | 2 | 4 | 7 | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | – | 7 | 7 | |
| | | | | | 3 | |
|
STEP 16: BRING DOWN
|
| | | 0 | 2 | 4 | 7 | |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | – | 7 | 7 | |
| | | | | | 3 | 3 |
STEP 17: DIVIDE 33 : 11 = 3 with a remainder of 0
|
| | | 0 | 2 | 4 | 7 | 3 |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | – | 7 | 7 | |
| | | | | | 3 | 3 |
STEP 18: MULTIPLY 3 · 11 = 33
|
| | | 0 | 2 | 4 | 7 | 3 |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | – | 7 | 7 | |
| | | | | | 3 | 3 |
| | | | | | 3 | 3 |
STEP 19: SUBTRACT 33 - 33 = 0
|
| | | 0 | 2 | 4 | 7 | 3 |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | – | 7 | 7 | |
| | | | | | 3 | 3 |
| | | | | – | 3 | 3 |
| | | | | | | 0 |
STEP 19: SUBTRACT 33 - 33 = 0
|
| | | 0 | 2 | 4 | 7 | 3 |
| 1 | 1 | 2 | 7 | 2 | 0 | 3 |
| | – | 0 | | | | |
| | | 2 | 7 | | | |
| | – | 2 | 2 | | | |
| | | | 5 | 2 | | |
| | | – | 4 | 4 | | |
| | | | | 8 | 0 | |
| | | | – | 7 | 7 | |
| | | | | | 3 | 3 |
| | | | | – | 3 | 3 |
| | | | | | | 0 |
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