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Question
What is the quotient and remainder when $ 35762 $ is divided by $ 975 $ ?
Answer
The quotient is 36 and the remainder is 662.
Explanation
|
Division Table
|
| | | | 0 | 0 | 0 | 3 | 6 |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | – | 2 | 9 | 2 | 5 | |
| | | | | 6 | 5 | 1 | 2 |
| | | | – | 5 | 8 | 5 | 0 |
| | | | | | 6 | 6 | 2 |
STEP 0: set up a division table
|
| | | | | | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
STEP 1: DIVIDE 3 : 975 = 0 with a remainder of 3
|
| | | | 0 | | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
STEP 2: MULTIPLY 0 · 975 = 0
|
| | | | 0 | | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | | 0 | | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | | 0 | | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | | | | |
|
STEP 4: BRING DOWN
|
| | | | 0 | | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
STEP 5: DIVIDE 35 : 975 = 0 with a remainder of 35
|
| | | | 0 | 0 | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
STEP 6: MULTIPLY 0 · 975 = 0
|
| | | | 0 | 0 | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | | 0 | | | |
STEP 7: SUBTRACT 35 - 0 = 35
|
| | | | 0 | 0 | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | | | |
|
STEP 8: BRING DOWN
|
| | | | 0 | 0 | | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
STEP 9: DIVIDE 357 : 975 = 0 with a remainder of 357
|
| | | | 0 | 0 | 0 | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
STEP 10: MULTIPLY 0 · 975 = 0
|
| | | | 0 | 0 | 0 | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | | 0 | | |
STEP 11: SUBTRACT 357 - 0 = 357
|
| | | | 0 | 0 | 0 | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | | |
|
STEP 12: BRING DOWN
|
| | | | 0 | 0 | 0 | | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
STEP 13: DIVIDE 3576 : 975 = 3 with a remainder of 651
|
| | | | 0 | 0 | 0 | 3 | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
STEP 14: MULTIPLY 3 · 975 = 2925
|
| | | | 0 | 0 | 0 | 3 | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | | 2 | 9 | 2 | 5 | |
STEP 15: SUBTRACT 3576 - 2925 = 651
|
| | | | 0 | 0 | 0 | 3 | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | – | 2 | 9 | 2 | 5 | |
| | | | | 6 | 5 | 1 | |
|
STEP 16: BRING DOWN
|
| | | | 0 | 0 | 0 | 3 | |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | – | 2 | 9 | 2 | 5 | |
| | | | | 6 | 5 | 1 | 2 |
STEP 17: DIVIDE 6512 : 975 = 6 with a remainder of 662
|
| | | | 0 | 0 | 0 | 3 | 6 |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | – | 2 | 9 | 2 | 5 | |
| | | | | 6 | 5 | 1 | 2 |
STEP 18: MULTIPLY 6 · 975 = 5850
|
| | | | 0 | 0 | 0 | 3 | 6 |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | – | 2 | 9 | 2 | 5 | |
| | | | | 6 | 5 | 1 | 2 |
| | | | | 5 | 8 | 5 | 0 |
STEP 19: SUBTRACT 6512 - 5850 = 662
|
| | | | 0 | 0 | 0 | 3 | 6 |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | – | 2 | 9 | 2 | 5 | |
| | | | | 6 | 5 | 1 | 2 |
| | | | – | 5 | 8 | 5 | 0 |
| | | | | | 6 | 6 | 2 |
STEP 19: SUBTRACT 6512 - 5850 = 662
|
| | | | 0 | 0 | 0 | 3 | 6 |
| 9 | 7 | 5 | 3 | 5 | 7 | 6 | 2 |
| | | – | 0 | | | | |
| | | | 3 | 5 | | | |
| | | | – | 0 | | | |
| | | | 3 | 5 | 7 | | |
| | | | | – | 0 | | |
| | | | 3 | 5 | 7 | 6 | |
| | | – | 2 | 9 | 2 | 5 | |
| | | | | 6 | 5 | 1 | 2 |
| | | | – | 5 | 8 | 5 | 0 |
| | | | | | 6 | 6 | 2 |
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