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Question
What is the quotient and remainder when $ 7837 $ is divided by $ 35 $ ?
Answer
The quotient is 223 and the remainder is 32.
Explanation
|
Division Table
|
| | | 0 | 2 | 2 | 3 |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | – | 7 | 0 | |
| | | | 1 | 3 | 7 |
| | | – | 1 | 0 | 5 |
| | | | | 3 | 2 |
STEP 0: set up a division table
|
| | | | | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
STEP 1: DIVIDE 7 : 35 = 0 with a remainder of 7
|
| | | 0 | | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
STEP 2: MULTIPLY 0 · 35 = 0
|
| | | 0 | | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | | 0 | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | | 0 | | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
STEP 5: DIVIDE 78 : 35 = 2 with a remainder of 8
|
| | | 0 | 2 | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
STEP 6: MULTIPLY 2 · 35 = 70
|
| | | 0 | 2 | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | | 7 | 0 | | |
STEP 7: SUBTRACT 78 - 70 = 8
|
| | | 0 | 2 | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
STEP 9: DIVIDE 83 : 35 = 2 with a remainder of 13
|
| | | 0 | 2 | 2 | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
STEP 10: MULTIPLY 2 · 35 = 70
|
| | | 0 | 2 | 2 | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | | 7 | 0 | |
STEP 11: SUBTRACT 83 - 70 = 13
|
| | | 0 | 2 | 2 | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | – | 7 | 0 | |
| | | | 1 | 3 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 2 | |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | – | 7 | 0 | |
| | | | 1 | 3 | 7 |
STEP 13: DIVIDE 137 : 35 = 3 with a remainder of 32
|
| | | 0 | 2 | 2 | 3 |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | – | 7 | 0 | |
| | | | 1 | 3 | 7 |
STEP 14: MULTIPLY 3 · 35 = 105
|
| | | 0 | 2 | 2 | 3 |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | – | 7 | 0 | |
| | | | 1 | 3 | 7 |
| | | | 1 | 0 | 5 |
STEP 15: SUBTRACT 137 - 105 = 32
|
| | | 0 | 2 | 2 | 3 |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | – | 7 | 0 | |
| | | | 1 | 3 | 7 |
| | | – | 1 | 0 | 5 |
| | | | | 3 | 2 |
STEP 15: SUBTRACT 137 - 105 = 32
|
| | | 0 | 2 | 2 | 3 |
| 3 | 5 | 7 | 8 | 3 | 7 |
| | – | 0 | | | |
| | | 7 | 8 | | |
| | – | 7 | 0 | | |
| | | | 8 | 3 | |
| | | – | 7 | 0 | |
| | | | 1 | 3 | 7 |
| | | – | 1 | 0 | 5 |
| | | | | 3 | 2 |
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