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Question
What is the quotient and remainder when $ 23666 $ is divided by $ 24 $ ?
Answer
The quotient is 986 and the remainder is 2.
Explanation
Division Table
|
| | 0 | 0 | 9 | 8 | 6 |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | – | 1 | 9 | 2 | |
| | | | 1 | 4 | 6 |
| | | – | 1 | 4 | 4 |
| | | | | | 2 |
STEP 0: set up a division table
|
| | | | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
STEP 1: DIVIDE 2 : 24 = 0 with a remainder of 2
|
| | 0 | | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
STEP 2: MULTIPLY 0 · 24 = 0
|
| | 0 | | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| | 0 | | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | 0 | | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | | | | |
STEP 4: BRING DOWN
|
| | 0 | | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
STEP 5: DIVIDE 23 : 24 = 0 with a remainder of 23
|
| | 0 | 0 | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
STEP 6: MULTIPLY 0 · 24 = 0
|
| | 0 | 0 | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | | 0 | | | |
STEP 7: SUBTRACT 23 - 0 = 23
|
| | 0 | 0 | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | | | |
STEP 8: BRING DOWN
|
| | 0 | 0 | | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
STEP 9: DIVIDE 236 : 24 = 9 with a remainder of 20
|
| | 0 | 0 | 9 | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
STEP 10: MULTIPLY 9 · 24 = 216
|
| | 0 | 0 | 9 | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| | 2 | 1 | 6 | | |
STEP 11: SUBTRACT 236 - 216 = 20
|
| | 0 | 0 | 9 | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | | |
STEP 12: BRING DOWN
|
| | 0 | 0 | 9 | | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
STEP 13: DIVIDE 206 : 24 = 8 with a remainder of 14
|
| | 0 | 0 | 9 | 8 | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
STEP 14: MULTIPLY 8 · 24 = 192
|
| | 0 | 0 | 9 | 8 | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | | 1 | 9 | 2 | |
STEP 15: SUBTRACT 206 - 192 = 14
|
| | 0 | 0 | 9 | 8 | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | – | 1 | 9 | 2 | |
| | | | 1 | 4 | |
STEP 16: BRING DOWN
|
| | 0 | 0 | 9 | 8 | |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | – | 1 | 9 | 2 | |
| | | | 1 | 4 | 6 |
STEP 17: DIVIDE 146 : 24 = 6 with a remainder of 2
|
| | 0 | 0 | 9 | 8 | 6 |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | – | 1 | 9 | 2 | |
| | | | 1 | 4 | 6 |
STEP 18: MULTIPLY 6 · 24 = 144
|
| | 0 | 0 | 9 | 8 | 6 |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | – | 1 | 9 | 2 | |
| | | | 1 | 4 | 6 |
| | | | 1 | 4 | 4 |
STEP 19: SUBTRACT 146 - 144 = 2
|
| | 0 | 0 | 9 | 8 | 6 |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | – | 1 | 9 | 2 | |
| | | | 1 | 4 | 6 |
| | | – | 1 | 4 | 4 |
| | | | | | 2 |
STEP 19: SUBTRACT 146 - 144 = 2
|
| | 0 | 0 | 9 | 8 | 6 |
2 | 4 | 2 | 3 | 6 | 6 | 6 |
| – | 0 | | | | |
| | 2 | 3 | | | |
| | – | 0 | | | |
| | 2 | 3 | 6 | | |
| – | 2 | 1 | 6 | | |
| | | 2 | 0 | 6 | |
| | – | 1 | 9 | 2 | |
| | | | 1 | 4 | 6 |
| | | – | 1 | 4 | 4 |
| | | | | | 2 |
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