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What is the quotient and remainder when $ 363681 $ is divided by $ 669 $ ?
Answer
The quotient is 543 and the remainder is 414.
Explanation
Division Table
|
| | | 0 | 0 | 0 | 5 | 4 | 3 |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | – | 2 | 6 | 7 | 6 | |
| | | | | 2 | 4 | 2 | 1 |
| | | | – | 2 | 0 | 0 | 7 |
| | | | | | 4 | 1 | 4 |
STEP 0: set up a division table
|
| | | | | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
STEP 1: DIVIDE 3 : 669 = 0 with a remainder of 3
|
| | | 0 | | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
STEP 2: MULTIPLY 0 · 669 = 0
|
| | | 0 | | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | | 0 | | | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | | | | | |
STEP 4: BRING DOWN
|
| | | 0 | | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
STEP 5: DIVIDE 36 : 669 = 0 with a remainder of 36
|
| | | 0 | 0 | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
STEP 6: MULTIPLY 0 · 669 = 0
|
| | | 0 | 0 | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | | 0 | | | | |
STEP 7: SUBTRACT 36 - 0 = 36
|
| | | 0 | 0 | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | | | | |
STEP 8: BRING DOWN
|
| | | 0 | 0 | | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
STEP 9: DIVIDE 363 : 669 = 0 with a remainder of 363
|
| | | 0 | 0 | 0 | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
STEP 10: MULTIPLY 0 · 669 = 0
|
| | | 0 | 0 | 0 | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | | 0 | | | |
STEP 11: SUBTRACT 363 - 0 = 363
|
| | | 0 | 0 | 0 | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | | | |
STEP 12: BRING DOWN
|
| | | 0 | 0 | 0 | | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
STEP 13: DIVIDE 3636 : 669 = 5 with a remainder of 291
|
| | | 0 | 0 | 0 | 5 | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
STEP 14: MULTIPLY 5 · 669 = 3345
|
| | | 0 | 0 | 0 | 5 | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | | 3 | 3 | 4 | 5 | | |
STEP 15: SUBTRACT 3636 - 3345 = 291
|
| | | 0 | 0 | 0 | 5 | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | | |
STEP 16: BRING DOWN
|
| | | 0 | 0 | 0 | 5 | | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
STEP 17: DIVIDE 2918 : 669 = 4 with a remainder of 242
|
| | | 0 | 0 | 0 | 5 | 4 | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
STEP 18: MULTIPLY 4 · 669 = 2676
|
| | | 0 | 0 | 0 | 5 | 4 | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | | 2 | 6 | 7 | 6 | |
STEP 19: SUBTRACT 2918 - 2676 = 242
|
| | | 0 | 0 | 0 | 5 | 4 | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | – | 2 | 6 | 7 | 6 | |
| | | | | 2 | 4 | 2 | |
STEP 20: BRING DOWN
|
| | | 0 | 0 | 0 | 5 | 4 | |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | – | 2 | 6 | 7 | 6 | |
| | | | | 2 | 4 | 2 | 1 |
STEP 21: DIVIDE 2421 : 669 = 3 with a remainder of 414
|
| | | 0 | 0 | 0 | 5 | 4 | 3 |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | – | 2 | 6 | 7 | 6 | |
| | | | | 2 | 4 | 2 | 1 |
STEP 22: MULTIPLY 3 · 669 = 2007
|
| | | 0 | 0 | 0 | 5 | 4 | 3 |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | – | 2 | 6 | 7 | 6 | |
| | | | | 2 | 4 | 2 | 1 |
| | | | | 2 | 0 | 0 | 7 |
STEP 23: SUBTRACT 2421 - 2007 = 414
|
| | | 0 | 0 | 0 | 5 | 4 | 3 |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | – | 2 | 6 | 7 | 6 | |
| | | | | 2 | 4 | 2 | 1 |
| | | | – | 2 | 0 | 0 | 7 |
| | | | | | 4 | 1 | 4 |
STEP 23: SUBTRACT 2421 - 2007 = 414
|
| | | 0 | 0 | 0 | 5 | 4 | 3 |
6 | 6 | 9 | 3 | 6 | 3 | 6 | 8 | 1 |
| | – | 0 | | | | | |
| | | 3 | 6 | | | | |
| | | – | 0 | | | | |
| | | 3 | 6 | 3 | | | |
| | | | – | 0 | | | |
| | | 3 | 6 | 3 | 6 | | |
| | – | 3 | 3 | 4 | 5 | | |
| | | | 2 | 9 | 1 | 8 | |
| | | – | 2 | 6 | 7 | 6 | |
| | | | | 2 | 4 | 2 | 1 |
| | | | – | 2 | 0 | 0 | 7 |
| | | | | | 4 | 1 | 4 |
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