Question
What is the quotient and remainder when $ 1350 $ is divided by $ 23 $ ?
Answer
The quotient is 58 and the remainder is 16.
Explanation
| Division Table | |||||
| 0 | 0 | 5 | 8 | ||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| – | 1 | 1 | 5 | ||
| 2 | 0 | 0 | |||
| – | 1 | 8 | 4 | ||
| 1 | 6 | ||||
|
STEP 0: set up a division table |
|||||
| 2 | 3 | 1 | 3 | 5 | 0 |
|
STEP 1: DIVIDE 1 : 23 = 0 with a remainder of 1 |
|||||
| 0 | |||||
| 2 | 3 | 1 | 3 | 5 | 0 |
|
STEP 2: MULTIPLY 0 · 23 = 0 |
|||||
| 0 | |||||
| 2 | 3 | 1 | 3 | 5 | 0 |
| 0 | |||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
|||||
| 0 | |||||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | |||||
| STEP 4: BRING DOWN | |||||
| 0 | |||||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
|
STEP 5: DIVIDE 13 : 23 = 0 with a remainder of 13 |
|||||
| 0 | 0 | ||||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
|
STEP 6: MULTIPLY 0 · 23 = 0 |
|||||
| 0 | 0 | ||||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| 0 | |||||
|
STEP 7: SUBTRACT 13 - 0 = 13 |
|||||
| 0 | 0 | ||||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | ||||
| STEP 8: BRING DOWN | |||||
| 0 | 0 | ||||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
|
STEP 9: DIVIDE 135 : 23 = 5 with a remainder of 20 |
|||||
| 0 | 0 | 5 | |||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
|
STEP 10: MULTIPLY 5 · 23 = 115 |
|||||
| 0 | 0 | 5 | |||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| 1 | 1 | 5 | |||
|
STEP 11: SUBTRACT 135 - 115 = 20 |
|||||
| 0 | 0 | 5 | |||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| – | 1 | 1 | 5 | ||
| 2 | 0 | ||||
| STEP 12: BRING DOWN | |||||
| 0 | 0 | 5 | |||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| – | 1 | 1 | 5 | ||
| 2 | 0 | 0 | |||
|
STEP 13: DIVIDE 200 : 23 = 8 with a remainder of 16 |
|||||
| 0 | 0 | 5 | 8 | ||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| – | 1 | 1 | 5 | ||
| 2 | 0 | 0 | |||
|
STEP 14: MULTIPLY 8 · 23 = 184 |
|||||
| 0 | 0 | 5 | 8 | ||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| – | 1 | 1 | 5 | ||
| 2 | 0 | 0 | |||
| 1 | 8 | 4 | |||
|
STEP 15: SUBTRACT 200 - 184 = 16 |
|||||
| 0 | 0 | 5 | 8 | ||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| – | 1 | 1 | 5 | ||
| 2 | 0 | 0 | |||
| – | 1 | 8 | 4 | ||
| 1 | 6 | ||||
|
STEP 15: SUBTRACT 200 - 184 = 16 |
|||||
| 0 | 0 | 5 | 8 | ||
| 2 | 3 | 1 | 3 | 5 | 0 |
| – | 0 | ||||
| 1 | 3 | ||||
| – | 0 | ||||
| 1 | 3 | 5 | |||
| – | 1 | 1 | 5 | ||
| 2 | 0 | 0 | |||
| – | 1 | 8 | 4 | ||
| 1 | 6 | ||||
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