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What is the quotient and remainder when $ 5604 $ is divided by $ 23 $ ?
Answer
The quotient is 243 and the remainder is 15.
Explanation
Division Table
|
| | 0 | 2 | 4 | 3 |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | – | 9 | 2 | |
| | | | 8 | 4 |
| | | – | 6 | 9 |
| | | | 1 | 5 |
STEP 0: set up a division table
|
| | | | | |
2 | 3 | 5 | 6 | 0 | 4 |
STEP 1: DIVIDE 5 : 23 = 0 with a remainder of 5
|
| | 0 | | | |
2 | 3 | 5 | 6 | 0 | 4 |
STEP 2: MULTIPLY 0 · 23 = 0
|
| | 0 | | | |
2 | 3 | 5 | 6 | 0 | 4 |
| | 0 | | | |
STEP 3: SUBTRACT 5 - 0 = 5
|
| | 0 | | | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
STEP 5: DIVIDE 56 : 23 = 2 with a remainder of 10
|
| | 0 | 2 | | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
STEP 6: MULTIPLY 2 · 23 = 46
|
| | 0 | 2 | | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| | 4 | 6 | | |
STEP 7: SUBTRACT 56 - 46 = 10
|
| | 0 | 2 | | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | | |
STEP 8: BRING DOWN
|
| | 0 | 2 | | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
STEP 9: DIVIDE 100 : 23 = 4 with a remainder of 8
|
| | 0 | 2 | 4 | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
STEP 10: MULTIPLY 4 · 23 = 92
|
| | 0 | 2 | 4 | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | | 9 | 2 | |
STEP 11: SUBTRACT 100 - 92 = 8
|
| | 0 | 2 | 4 | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | – | 9 | 2 | |
| | | | 8 | |
STEP 12: BRING DOWN
|
| | 0 | 2 | 4 | |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | – | 9 | 2 | |
| | | | 8 | 4 |
STEP 13: DIVIDE 84 : 23 = 3 with a remainder of 15
|
| | 0 | 2 | 4 | 3 |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | – | 9 | 2 | |
| | | | 8 | 4 |
STEP 14: MULTIPLY 3 · 23 = 69
|
| | 0 | 2 | 4 | 3 |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | – | 9 | 2 | |
| | | | 8 | 4 |
| | | | 6 | 9 |
STEP 15: SUBTRACT 84 - 69 = 15
|
| | 0 | 2 | 4 | 3 |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | – | 9 | 2 | |
| | | | 8 | 4 |
| | | – | 6 | 9 |
| | | | 1 | 5 |
STEP 15: SUBTRACT 84 - 69 = 15
|
| | 0 | 2 | 4 | 3 |
2 | 3 | 5 | 6 | 0 | 4 |
| – | 0 | | | |
| | 5 | 6 | | |
| – | 4 | 6 | | |
| | 1 | 0 | 0 | |
| | – | 9 | 2 | |
| | | | 8 | 4 |
| | | – | 6 | 9 |
| | | | 1 | 5 |
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