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What is the quotient and remainder when $ 3765 $ is divided by $ 45 $ ?
Answer
The quotient is 83 and the remainder is 30.
Explanation
Division Table
|
| | 0 | 0 | 8 | 3 |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| – | 3 | 6 | 0 | |
| | | 1 | 6 | 5 |
| | – | 1 | 3 | 5 |
| | | | 3 | 0 |
STEP 0: set up a division table
|
| | | | | |
4 | 5 | 3 | 7 | 6 | 5 |
STEP 1: DIVIDE 3 : 45 = 0 with a remainder of 3
|
| | 0 | | | |
4 | 5 | 3 | 7 | 6 | 5 |
STEP 2: MULTIPLY 0 · 45 = 0
|
| | 0 | | | |
4 | 5 | 3 | 7 | 6 | 5 |
| | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | 0 | | | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
STEP 5: DIVIDE 37 : 45 = 0 with a remainder of 37
|
| | 0 | 0 | | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
STEP 6: MULTIPLY 0 · 45 = 0
|
| | 0 | 0 | | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | | 0 | | |
STEP 7: SUBTRACT 37 - 0 = 37
|
| | 0 | 0 | | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | | |
STEP 8: BRING DOWN
|
| | 0 | 0 | | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
STEP 9: DIVIDE 376 : 45 = 8 with a remainder of 16
|
| | 0 | 0 | 8 | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
STEP 10: MULTIPLY 8 · 45 = 360
|
| | 0 | 0 | 8 | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| | 3 | 6 | 0 | |
STEP 11: SUBTRACT 376 - 360 = 16
|
| | 0 | 0 | 8 | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| – | 3 | 6 | 0 | |
| | | 1 | 6 | |
STEP 12: BRING DOWN
|
| | 0 | 0 | 8 | |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| – | 3 | 6 | 0 | |
| | | 1 | 6 | 5 |
STEP 13: DIVIDE 165 : 45 = 3 with a remainder of 30
|
| | 0 | 0 | 8 | 3 |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| – | 3 | 6 | 0 | |
| | | 1 | 6 | 5 |
STEP 14: MULTIPLY 3 · 45 = 135
|
| | 0 | 0 | 8 | 3 |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| – | 3 | 6 | 0 | |
| | | 1 | 6 | 5 |
| | | 1 | 3 | 5 |
STEP 15: SUBTRACT 165 - 135 = 30
|
| | 0 | 0 | 8 | 3 |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| – | 3 | 6 | 0 | |
| | | 1 | 6 | 5 |
| | – | 1 | 3 | 5 |
| | | | 3 | 0 |
STEP 15: SUBTRACT 165 - 135 = 30
|
| | 0 | 0 | 8 | 3 |
4 | 5 | 3 | 7 | 6 | 5 |
| – | 0 | | | |
| | 3 | 7 | | |
| | – | 0 | | |
| | 3 | 7 | 6 | |
| – | 3 | 6 | 0 | |
| | | 1 | 6 | 5 |
| | – | 1 | 3 | 5 |
| | | | 3 | 0 |
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