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Question
What is the quotient and remainder when $ 827 $ is divided by $ 26 $ ?
Answer
The quotient is 31 and the remainder is 21.
Explanation
|
Division Table
|
| | | 0 | 3 | 1 |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | – | 7 | 8 | |
| | | | 4 | 7 |
| | | – | 2 | 6 |
| | | | 2 | 1 |
STEP 0: set up a division table
|
| | | | | |
| 2 | 6 | 8 | 2 | 7 |
STEP 1: DIVIDE 8 : 26 = 0 with a remainder of 8
|
| | | 0 | | |
| 2 | 6 | 8 | 2 | 7 |
STEP 2: MULTIPLY 0 · 26 = 0
|
| | | 0 | | |
| 2 | 6 | 8 | 2 | 7 |
| | | 0 | | |
STEP 3: SUBTRACT 8 - 0 = 8
|
| | | 0 | | |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
STEP 5: DIVIDE 82 : 26 = 3 with a remainder of 4
|
| | | 0 | 3 | |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
STEP 6: MULTIPLY 3 · 26 = 78
|
| | | 0 | 3 | |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | | 7 | 8 | |
STEP 7: SUBTRACT 82 - 78 = 4
|
| | | 0 | 3 | |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | – | 7 | 8 | |
| | | | 4 | |
|
STEP 8: BRING DOWN
|
| | | 0 | 3 | |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | – | 7 | 8 | |
| | | | 4 | 7 |
STEP 9: DIVIDE 47 : 26 = 1 with a remainder of 21
|
| | | 0 | 3 | 1 |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | – | 7 | 8 | |
| | | | 4 | 7 |
STEP 10: MULTIPLY 1 · 26 = 26
|
| | | 0 | 3 | 1 |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | – | 7 | 8 | |
| | | | 4 | 7 |
| | | | 2 | 6 |
STEP 11: SUBTRACT 47 - 26 = 21
|
| | | 0 | 3 | 1 |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | – | 7 | 8 | |
| | | | 4 | 7 |
| | | – | 2 | 6 |
| | | | 2 | 1 |
STEP 11: SUBTRACT 47 - 26 = 21
|
| | | 0 | 3 | 1 |
| 2 | 6 | 8 | 2 | 7 |
| | – | 0 | | |
| | | 8 | 2 | |
| | – | 7 | 8 | |
| | | | 4 | 7 |
| | | – | 2 | 6 |
| | | | 2 | 1 |
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