Question
What is the quotient and remainder when $ 1453 $ is divided by $ 31 $ ?
Answer
The quotient is 46 and the remainder is 27.
Explanation
| Division Table | |||||
| 0 | 0 | 4 | 6 | ||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| – | 1 | 2 | 4 | ||
| 2 | 1 | 3 | |||
| – | 1 | 8 | 6 | ||
| 2 | 7 | ||||
|
STEP 0: set up a division table |
|||||
| 3 | 1 | 1 | 4 | 5 | 3 |
|
STEP 1: DIVIDE 1 : 31 = 0 with a remainder of 1 |
|||||
| 0 | |||||
| 3 | 1 | 1 | 4 | 5 | 3 |
|
STEP 2: MULTIPLY 0 · 31 = 0 |
|||||
| 0 | |||||
| 3 | 1 | 1 | 4 | 5 | 3 |
| 0 | |||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
|||||
| 0 | |||||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | |||||
| STEP 4: BRING DOWN | |||||
| 0 | |||||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
|
STEP 5: DIVIDE 14 : 31 = 0 with a remainder of 14 |
|||||
| 0 | 0 | ||||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
|
STEP 6: MULTIPLY 0 · 31 = 0 |
|||||
| 0 | 0 | ||||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| 0 | |||||
|
STEP 7: SUBTRACT 14 - 0 = 14 |
|||||
| 0 | 0 | ||||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | ||||
| STEP 8: BRING DOWN | |||||
| 0 | 0 | ||||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
|
STEP 9: DIVIDE 145 : 31 = 4 with a remainder of 21 |
|||||
| 0 | 0 | 4 | |||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
|
STEP 10: MULTIPLY 4 · 31 = 124 |
|||||
| 0 | 0 | 4 | |||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| 1 | 2 | 4 | |||
|
STEP 11: SUBTRACT 145 - 124 = 21 |
|||||
| 0 | 0 | 4 | |||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| – | 1 | 2 | 4 | ||
| 2 | 1 | ||||
| STEP 12: BRING DOWN | |||||
| 0 | 0 | 4 | |||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| – | 1 | 2 | 4 | ||
| 2 | 1 | 3 | |||
|
STEP 13: DIVIDE 213 : 31 = 6 with a remainder of 27 |
|||||
| 0 | 0 | 4 | 6 | ||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| – | 1 | 2 | 4 | ||
| 2 | 1 | 3 | |||
|
STEP 14: MULTIPLY 6 · 31 = 186 |
|||||
| 0 | 0 | 4 | 6 | ||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| – | 1 | 2 | 4 | ||
| 2 | 1 | 3 | |||
| 1 | 8 | 6 | |||
|
STEP 15: SUBTRACT 213 - 186 = 27 |
|||||
| 0 | 0 | 4 | 6 | ||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| – | 1 | 2 | 4 | ||
| 2 | 1 | 3 | |||
| – | 1 | 8 | 6 | ||
| 2 | 7 | ||||
|
STEP 15: SUBTRACT 213 - 186 = 27 |
|||||
| 0 | 0 | 4 | 6 | ||
| 3 | 1 | 1 | 4 | 5 | 3 |
| – | 0 | ||||
| 1 | 4 | ||||
| – | 0 | ||||
| 1 | 4 | 5 | |||
| – | 1 | 2 | 4 | ||
| 2 | 1 | 3 | |||
| – | 1 | 8 | 6 | ||
| 2 | 7 | ||||
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