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Question
What is the quotient and remainder when $ 1582 $ is divided by $ 67 $ ?
Answer
The quotient is 23 and the remainder is 41.
Explanation
|
Division Table
|
| | | 0 | 0 | 2 | 3 |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | – | 1 | 3 | 4 | |
| | | | 2 | 4 | 2 |
| | | – | 2 | 0 | 1 |
| | | | | 4 | 1 |
STEP 0: set up a division table
|
| | | | | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
STEP 1: DIVIDE 1 : 67 = 0 with a remainder of 1
|
| | | 0 | | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
STEP 2: MULTIPLY 0 · 67 = 0
|
| | | 0 | | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | | 0 | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | | 0 | | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
STEP 5: DIVIDE 15 : 67 = 0 with a remainder of 15
|
| | | 0 | 0 | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
STEP 6: MULTIPLY 0 · 67 = 0
|
| | | 0 | 0 | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 15 - 0 = 15
|
| | | 0 | 0 | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
STEP 9: DIVIDE 158 : 67 = 2 with a remainder of 24
|
| | | 0 | 0 | 2 | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
STEP 10: MULTIPLY 2 · 67 = 134
|
| | | 0 | 0 | 2 | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | | 1 | 3 | 4 | |
STEP 11: SUBTRACT 158 - 134 = 24
|
| | | 0 | 0 | 2 | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | – | 1 | 3 | 4 | |
| | | | 2 | 4 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 0 | 2 | |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | – | 1 | 3 | 4 | |
| | | | 2 | 4 | 2 |
STEP 13: DIVIDE 242 : 67 = 3 with a remainder of 41
|
| | | 0 | 0 | 2 | 3 |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | – | 1 | 3 | 4 | |
| | | | 2 | 4 | 2 |
STEP 14: MULTIPLY 3 · 67 = 201
|
| | | 0 | 0 | 2 | 3 |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | – | 1 | 3 | 4 | |
| | | | 2 | 4 | 2 |
| | | | 2 | 0 | 1 |
STEP 15: SUBTRACT 242 - 201 = 41
|
| | | 0 | 0 | 2 | 3 |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | – | 1 | 3 | 4 | |
| | | | 2 | 4 | 2 |
| | | – | 2 | 0 | 1 |
| | | | | 4 | 1 |
STEP 15: SUBTRACT 242 - 201 = 41
|
| | | 0 | 0 | 2 | 3 |
| 6 | 7 | 1 | 5 | 8 | 2 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | – | 0 | | |
| | | 1 | 5 | 8 | |
| | – | 1 | 3 | 4 | |
| | | | 2 | 4 | 2 |
| | | – | 2 | 0 | 1 |
| | | | | 4 | 1 |
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