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Question
What is the quotient and remainder when $ 5263 $ is divided by $ 42 $ ?
Answer
The quotient is 125 and the remainder is 13.
Explanation
|
Division Table
|
| | | 0 | 1 | 2 | 5 |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | – | 8 | 4 | |
| | | | 2 | 2 | 3 |
| | | – | 2 | 1 | 0 |
| | | | | 1 | 3 |
STEP 0: set up a division table
|
| | | | | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
STEP 1: DIVIDE 5 : 42 = 0 with a remainder of 5
|
| | | 0 | | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
STEP 2: MULTIPLY 0 · 42 = 0
|
| | | 0 | | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | | 0 | | | |
STEP 3: SUBTRACT 5 - 0 = 5
|
| | | 0 | | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
STEP 5: DIVIDE 52 : 42 = 1 with a remainder of 10
|
| | | 0 | 1 | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
STEP 6: MULTIPLY 1 · 42 = 42
|
| | | 0 | 1 | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | | 4 | 2 | | |
STEP 7: SUBTRACT 52 - 42 = 10
|
| | | 0 | 1 | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
STEP 9: DIVIDE 106 : 42 = 2 with a remainder of 22
|
| | | 0 | 1 | 2 | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
STEP 10: MULTIPLY 2 · 42 = 84
|
| | | 0 | 1 | 2 | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | | 8 | 4 | |
STEP 11: SUBTRACT 106 - 84 = 22
|
| | | 0 | 1 | 2 | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | – | 8 | 4 | |
| | | | 2 | 2 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 2 | |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | – | 8 | 4 | |
| | | | 2 | 2 | 3 |
STEP 13: DIVIDE 223 : 42 = 5 with a remainder of 13
|
| | | 0 | 1 | 2 | 5 |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | – | 8 | 4 | |
| | | | 2 | 2 | 3 |
STEP 14: MULTIPLY 5 · 42 = 210
|
| | | 0 | 1 | 2 | 5 |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | – | 8 | 4 | |
| | | | 2 | 2 | 3 |
| | | | 2 | 1 | 0 |
STEP 15: SUBTRACT 223 - 210 = 13
|
| | | 0 | 1 | 2 | 5 |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | – | 8 | 4 | |
| | | | 2 | 2 | 3 |
| | | – | 2 | 1 | 0 |
| | | | | 1 | 3 |
STEP 15: SUBTRACT 223 - 210 = 13
|
| | | 0 | 1 | 2 | 5 |
| 4 | 2 | 5 | 2 | 6 | 3 |
| | – | 0 | | | |
| | | 5 | 2 | | |
| | – | 4 | 2 | | |
| | | 1 | 0 | 6 | |
| | | – | 8 | 4 | |
| | | | 2 | 2 | 3 |
| | | – | 2 | 1 | 0 |
| | | | | 1 | 3 |
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