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Question
What is the quotient and remainder when $ 76055 $ is divided by $ 26 $ ?
Answer
The quotient is 2925 and the remainder is 5.
Explanation
|
Division Table
|
| | | 0 | 2 | 9 | 2 | 5 |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 3 | 5 |
| | | | – | 1 | 3 | 0 |
| | | | | | | 5 |
STEP 0: set up a division table
|
| | | | | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
STEP 1: DIVIDE 7 : 26 = 0 with a remainder of 7
|
| | | 0 | | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
STEP 2: MULTIPLY 0 · 26 = 0
|
| | | 0 | | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | | 0 | | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | | 0 | | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
STEP 5: DIVIDE 76 : 26 = 2 with a remainder of 24
|
| | | 0 | 2 | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
STEP 6: MULTIPLY 2 · 26 = 52
|
| | | 0 | 2 | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | | 5 | 2 | | | |
STEP 7: SUBTRACT 76 - 52 = 24
|
| | | 0 | 2 | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
STEP 9: DIVIDE 240 : 26 = 9 with a remainder of 6
|
| | | 0 | 2 | 9 | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
STEP 10: MULTIPLY 9 · 26 = 234
|
| | | 0 | 2 | 9 | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | | 2 | 3 | 4 | | |
STEP 11: SUBTRACT 240 - 234 = 6
|
| | | 0 | 2 | 9 | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 9 | | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
STEP 13: DIVIDE 65 : 26 = 2 with a remainder of 13
|
| | | 0 | 2 | 9 | 2 | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
STEP 14: MULTIPLY 2 · 26 = 52
|
| | | 0 | 2 | 9 | 2 | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | | 5 | 2 | |
STEP 15: SUBTRACT 65 - 52 = 13
|
| | | 0 | 2 | 9 | 2 | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 3 | |
|
STEP 16: BRING DOWN
|
| | | 0 | 2 | 9 | 2 | |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 3 | 5 |
STEP 17: DIVIDE 135 : 26 = 5 with a remainder of 5
|
| | | 0 | 2 | 9 | 2 | 5 |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 3 | 5 |
STEP 18: MULTIPLY 5 · 26 = 130
|
| | | 0 | 2 | 9 | 2 | 5 |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 3 | 5 |
| | | | | 1 | 3 | 0 |
STEP 19: SUBTRACT 135 - 130 = 5
|
| | | 0 | 2 | 9 | 2 | 5 |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 3 | 5 |
| | | | – | 1 | 3 | 0 |
| | | | | | | 5 |
STEP 19: SUBTRACT 135 - 130 = 5
|
| | | 0 | 2 | 9 | 2 | 5 |
| 2 | 6 | 7 | 6 | 0 | 5 | 5 |
| | – | 0 | | | | |
| | | 7 | 6 | | | |
| | – | 5 | 2 | | | |
| | | 2 | 4 | 0 | | |
| | – | 2 | 3 | 4 | | |
| | | | | 6 | 5 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 3 | 5 |
| | | | – | 1 | 3 | 0 |
| | | | | | | 5 |
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