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What is the quotient and remainder when $ 1634 $ is divided by $ 231 $ ?
Answer
The quotient is 7 and the remainder is 17.
Explanation
Division Table
|
| | | 0 | 0 | 0 | 7 |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | – | 0 | |
| | | 1 | 6 | 3 | 4 |
| | – | 1 | 6 | 1 | 7 |
| | | | | 1 | 7 |
STEP 0: set up a division table
|
| | | | | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
STEP 1: DIVIDE 1 : 231 = 0 with a remainder of 1
|
| | | 0 | | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
STEP 2: MULTIPLY 0 · 231 = 0
|
| | | 0 | | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | | 0 | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | | 0 | | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | | | |
STEP 4: BRING DOWN
|
| | | 0 | | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
STEP 5: DIVIDE 16 : 231 = 0 with a remainder of 16
|
| | | 0 | 0 | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
STEP 6: MULTIPLY 0 · 231 = 0
|
| | | 0 | 0 | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 16 - 0 = 16
|
| | | 0 | 0 | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | | |
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
STEP 9: DIVIDE 163 : 231 = 0 with a remainder of 163
|
| | | 0 | 0 | 0 | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
STEP 10: MULTIPLY 0 · 231 = 0
|
| | | 0 | 0 | 0 | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | | 0 | |
STEP 11: SUBTRACT 163 - 0 = 163
|
| | | 0 | 0 | 0 | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | – | 0 | |
| | | 1 | 6 | 3 | |
STEP 12: BRING DOWN
|
| | | 0 | 0 | 0 | |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | – | 0 | |
| | | 1 | 6 | 3 | 4 |
STEP 13: DIVIDE 1634 : 231 = 7 with a remainder of 17
|
| | | 0 | 0 | 0 | 7 |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | – | 0 | |
| | | 1 | 6 | 3 | 4 |
STEP 14: MULTIPLY 7 · 231 = 1617
|
| | | 0 | 0 | 0 | 7 |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | – | 0 | |
| | | 1 | 6 | 3 | 4 |
| | | 1 | 6 | 1 | 7 |
STEP 15: SUBTRACT 1634 - 1617 = 17
|
| | | 0 | 0 | 0 | 7 |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | – | 0 | |
| | | 1 | 6 | 3 | 4 |
| | – | 1 | 6 | 1 | 7 |
| | | | | 1 | 7 |
STEP 15: SUBTRACT 1634 - 1617 = 17
|
| | | 0 | 0 | 0 | 7 |
2 | 3 | 1 | 1 | 6 | 3 | 4 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | – | 0 | | |
| | | 1 | 6 | 3 | |
| | | | – | 0 | |
| | | 1 | 6 | 3 | 4 |
| | – | 1 | 6 | 1 | 7 |
| | | | | 1 | 7 |
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