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Question
What is the quotient and remainder when $ 5745 $ is divided by $ 34 $ ?
Answer
The quotient is 168 and the remainder is 33.
Explanation
|
Division Table
|
| | | 0 | 1 | 6 | 8 |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | – | 2 | 0 | 4 | |
| | | | 3 | 0 | 5 |
| | | – | 2 | 7 | 2 |
| | | | | 3 | 3 |
STEP 0: set up a division table
|
| | | | | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
STEP 1: DIVIDE 5 : 34 = 0 with a remainder of 5
|
| | | 0 | | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
STEP 2: MULTIPLY 0 · 34 = 0
|
| | | 0 | | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | | 0 | | | |
STEP 3: SUBTRACT 5 - 0 = 5
|
| | | 0 | | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
STEP 5: DIVIDE 57 : 34 = 1 with a remainder of 23
|
| | | 0 | 1 | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
STEP 6: MULTIPLY 1 · 34 = 34
|
| | | 0 | 1 | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | | 3 | 4 | | |
STEP 7: SUBTRACT 57 - 34 = 23
|
| | | 0 | 1 | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
STEP 9: DIVIDE 234 : 34 = 6 with a remainder of 30
|
| | | 0 | 1 | 6 | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
STEP 10: MULTIPLY 6 · 34 = 204
|
| | | 0 | 1 | 6 | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | | 2 | 0 | 4 | |
STEP 11: SUBTRACT 234 - 204 = 30
|
| | | 0 | 1 | 6 | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | – | 2 | 0 | 4 | |
| | | | 3 | 0 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 6 | |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | – | 2 | 0 | 4 | |
| | | | 3 | 0 | 5 |
STEP 13: DIVIDE 305 : 34 = 8 with a remainder of 33
|
| | | 0 | 1 | 6 | 8 |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | – | 2 | 0 | 4 | |
| | | | 3 | 0 | 5 |
STEP 14: MULTIPLY 8 · 34 = 272
|
| | | 0 | 1 | 6 | 8 |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | – | 2 | 0 | 4 | |
| | | | 3 | 0 | 5 |
| | | | 2 | 7 | 2 |
STEP 15: SUBTRACT 305 - 272 = 33
|
| | | 0 | 1 | 6 | 8 |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | – | 2 | 0 | 4 | |
| | | | 3 | 0 | 5 |
| | | – | 2 | 7 | 2 |
| | | | | 3 | 3 |
STEP 15: SUBTRACT 305 - 272 = 33
|
| | | 0 | 1 | 6 | 8 |
| 3 | 4 | 5 | 7 | 4 | 5 |
| | – | 0 | | | |
| | | 5 | 7 | | |
| | – | 3 | 4 | | |
| | | 2 | 3 | 4 | |
| | – | 2 | 0 | 4 | |
| | | | 3 | 0 | 5 |
| | | – | 2 | 7 | 2 |
| | | | | 3 | 3 |
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