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Question
What is the quotient and remainder when $ 3726 $ is divided by $ 35 $ ?
Answer
The quotient is 106 and the remainder is 16.
Explanation
|
Division Table
|
| | | 0 | 1 | 0 | 6 |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | – | 0 | |
| | | | 2 | 2 | 6 |
| | | – | 2 | 1 | 0 |
| | | | | 1 | 6 |
STEP 0: set up a division table
|
| | | | | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
STEP 1: DIVIDE 3 : 35 = 0 with a remainder of 3
|
| | | 0 | | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
STEP 2: MULTIPLY 0 · 35 = 0
|
| | | 0 | | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
STEP 5: DIVIDE 37 : 35 = 1 with a remainder of 2
|
| | | 0 | 1 | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
STEP 6: MULTIPLY 1 · 35 = 35
|
| | | 0 | 1 | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | | 3 | 5 | | |
STEP 7: SUBTRACT 37 - 35 = 2
|
| | | 0 | 1 | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
STEP 9: DIVIDE 22 : 35 = 0 with a remainder of 22
|
| | | 0 | 1 | 0 | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
STEP 10: MULTIPLY 0 · 35 = 0
|
| | | 0 | 1 | 0 | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | | 0 | |
STEP 11: SUBTRACT 22 - 0 = 22
|
| | | 0 | 1 | 0 | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | – | 0 | |
| | | | 2 | 2 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 0 | |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | – | 0 | |
| | | | 2 | 2 | 6 |
STEP 13: DIVIDE 226 : 35 = 6 with a remainder of 16
|
| | | 0 | 1 | 0 | 6 |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | – | 0 | |
| | | | 2 | 2 | 6 |
STEP 14: MULTIPLY 6 · 35 = 210
|
| | | 0 | 1 | 0 | 6 |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | – | 0 | |
| | | | 2 | 2 | 6 |
| | | | 2 | 1 | 0 |
STEP 15: SUBTRACT 226 - 210 = 16
|
| | | 0 | 1 | 0 | 6 |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | – | 0 | |
| | | | 2 | 2 | 6 |
| | | – | 2 | 1 | 0 |
| | | | | 1 | 6 |
STEP 15: SUBTRACT 226 - 210 = 16
|
| | | 0 | 1 | 0 | 6 |
| 3 | 5 | 3 | 7 | 2 | 6 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 3 | 5 | | |
| | | | 2 | 2 | |
| | | | – | 0 | |
| | | | 2 | 2 | 6 |
| | | – | 2 | 1 | 0 |
| | | | | 1 | 6 |
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