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What is the quotient and remainder when $ 1165 $ is divided by $ 106 $ ?
Answer
The quotient is 10 and the remainder is 105.
Explanation
Division Table
|
| | | 0 | 0 | 1 | 0 |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | – | 1 | 0 | 6 | |
| | | | 1 | 0 | 5 |
| | | | | – | 0 |
| | | | 1 | 0 | 5 |
STEP 0: set up a division table
|
| | | | | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
STEP 1: DIVIDE 1 : 106 = 0 with a remainder of 1
|
| | | 0 | | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
STEP 2: MULTIPLY 0 · 106 = 0
|
| | | 0 | | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | | 0 | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | | 0 | | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | | | |
STEP 4: BRING DOWN
|
| | | 0 | | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
STEP 5: DIVIDE 11 : 106 = 0 with a remainder of 11
|
| | | 0 | 0 | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
STEP 6: MULTIPLY 0 · 106 = 0
|
| | | 0 | 0 | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 11 - 0 = 11
|
| | | 0 | 0 | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | | |
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
STEP 9: DIVIDE 116 : 106 = 1 with a remainder of 10
|
| | | 0 | 0 | 1 | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
STEP 10: MULTIPLY 1 · 106 = 106
|
| | | 0 | 0 | 1 | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | | 1 | 0 | 6 | |
STEP 11: SUBTRACT 116 - 106 = 10
|
| | | 0 | 0 | 1 | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | – | 1 | 0 | 6 | |
| | | | 1 | 0 | |
STEP 12: BRING DOWN
|
| | | 0 | 0 | 1 | |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | – | 1 | 0 | 6 | |
| | | | 1 | 0 | 5 |
STEP 13: DIVIDE 105 : 106 = 0 with a remainder of 105
|
| | | 0 | 0 | 1 | 0 |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | – | 1 | 0 | 6 | |
| | | | 1 | 0 | 5 |
STEP 14: MULTIPLY 0 · 106 = 0
|
| | | 0 | 0 | 1 | 0 |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | – | 1 | 0 | 6 | |
| | | | 1 | 0 | 5 |
| | | | | | 0 |
STEP 15: SUBTRACT 105 - 0 = 105
|
| | | 0 | 0 | 1 | 0 |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | – | 1 | 0 | 6 | |
| | | | 1 | 0 | 5 |
| | | | | – | 0 |
| | | | 1 | 0 | 5 |
STEP 15: SUBTRACT 105 - 0 = 105
|
| | | 0 | 0 | 1 | 0 |
1 | 0 | 6 | 1 | 1 | 6 | 5 |
| | – | 0 | | | |
| | | 1 | 1 | | |
| | | – | 0 | | |
| | | 1 | 1 | 6 | |
| | – | 1 | 0 | 6 | |
| | | | 1 | 0 | 5 |
| | | | | – | 0 |
| | | | 1 | 0 | 5 |
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