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Question
What is the quotient and remainder when $ 24674 $ is divided by $ 117 $ ?
Answer
The quotient is 210 and the remainder is 104.
Explanation
|
Division Table
|
| | | | 0 | 0 | 2 | 1 | 0 |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | – | 1 | 1 | 7 | |
| | | | | | 1 | 0 | 4 |
| | | | | | | – | 0 |
| | | | | | 1 | 0 | 4 |
STEP 0: set up a division table
|
| | | | | | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
STEP 1: DIVIDE 2 : 117 = 0 with a remainder of 2
|
| | | | 0 | | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
STEP 2: MULTIPLY 0 · 117 = 0
|
| | | | 0 | | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | | 0 | | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | | 0 | | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | | | | |
|
STEP 4: BRING DOWN
|
| | | | 0 | | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
STEP 5: DIVIDE 24 : 117 = 0 with a remainder of 24
|
| | | | 0 | 0 | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
STEP 6: MULTIPLY 0 · 117 = 0
|
| | | | 0 | 0 | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | | 0 | | | |
STEP 7: SUBTRACT 24 - 0 = 24
|
| | | | 0 | 0 | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | | | |
|
STEP 8: BRING DOWN
|
| | | | 0 | 0 | | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
STEP 9: DIVIDE 246 : 117 = 2 with a remainder of 12
|
| | | | 0 | 0 | 2 | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
STEP 10: MULTIPLY 2 · 117 = 234
|
| | | | 0 | 0 | 2 | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | | 2 | 3 | 4 | | |
STEP 11: SUBTRACT 246 - 234 = 12
|
| | | | 0 | 0 | 2 | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | | |
|
STEP 12: BRING DOWN
|
| | | | 0 | 0 | 2 | | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
STEP 13: DIVIDE 127 : 117 = 1 with a remainder of 10
|
| | | | 0 | 0 | 2 | 1 | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
STEP 14: MULTIPLY 1 · 117 = 117
|
| | | | 0 | 0 | 2 | 1 | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | | 1 | 1 | 7 | |
STEP 15: SUBTRACT 127 - 117 = 10
|
| | | | 0 | 0 | 2 | 1 | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | – | 1 | 1 | 7 | |
| | | | | | 1 | 0 | |
|
STEP 16: BRING DOWN
|
| | | | 0 | 0 | 2 | 1 | |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | – | 1 | 1 | 7 | |
| | | | | | 1 | 0 | 4 |
STEP 17: DIVIDE 104 : 117 = 0 with a remainder of 104
|
| | | | 0 | 0 | 2 | 1 | 0 |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | – | 1 | 1 | 7 | |
| | | | | | 1 | 0 | 4 |
STEP 18: MULTIPLY 0 · 117 = 0
|
| | | | 0 | 0 | 2 | 1 | 0 |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | – | 1 | 1 | 7 | |
| | | | | | 1 | 0 | 4 |
| | | | | | | | 0 |
STEP 19: SUBTRACT 104 - 0 = 104
|
| | | | 0 | 0 | 2 | 1 | 0 |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | – | 1 | 1 | 7 | |
| | | | | | 1 | 0 | 4 |
| | | | | | | – | 0 |
| | | | | | 1 | 0 | 4 |
STEP 19: SUBTRACT 104 - 0 = 104
|
| | | | 0 | 0 | 2 | 1 | 0 |
| 1 | 1 | 7 | 2 | 4 | 6 | 7 | 4 |
| | | – | 0 | | | | |
| | | | 2 | 4 | | | |
| | | | – | 0 | | | |
| | | | 2 | 4 | 6 | | |
| | | – | 2 | 3 | 4 | | |
| | | | | 1 | 2 | 7 | |
| | | | – | 1 | 1 | 7 | |
| | | | | | 1 | 0 | 4 |
| | | | | | | – | 0 |
| | | | | | 1 | 0 | 4 |
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