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Question
What is the quotient and remainder when $ 61982 $ is divided by $ 23 $ ?
Answer
The quotient is 2694 and the remainder is 20.
Explanation
|
Division Table
|
| | | 0 | 2 | 6 | 9 | 4 |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | – | 2 | 0 | 7 | |
| | | | | 1 | 1 | 2 |
| | | | | – | 9 | 2 |
| | | | | | 2 | 0 |
STEP 0: set up a division table
|
| | | | | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
STEP 1: DIVIDE 6 : 23 = 0 with a remainder of 6
|
| | | 0 | | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
STEP 2: MULTIPLY 0 · 23 = 0
|
| | | 0 | | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | | 0 | | | | |
STEP 3: SUBTRACT 6 - 0 = 6
|
| | | 0 | | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
STEP 5: DIVIDE 61 : 23 = 2 with a remainder of 15
|
| | | 0 | 2 | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
STEP 6: MULTIPLY 2 · 23 = 46
|
| | | 0 | 2 | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | | 4 | 6 | | | |
STEP 7: SUBTRACT 61 - 46 = 15
|
| | | 0 | 2 | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
STEP 9: DIVIDE 159 : 23 = 6 with a remainder of 21
|
| | | 0 | 2 | 6 | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
STEP 10: MULTIPLY 6 · 23 = 138
|
| | | 0 | 2 | 6 | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | | 1 | 3 | 8 | | |
STEP 11: SUBTRACT 159 - 138 = 21
|
| | | 0 | 2 | 6 | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 6 | | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
STEP 13: DIVIDE 218 : 23 = 9 with a remainder of 11
|
| | | 0 | 2 | 6 | 9 | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
STEP 14: MULTIPLY 9 · 23 = 207
|
| | | 0 | 2 | 6 | 9 | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | | 2 | 0 | 7 | |
STEP 15: SUBTRACT 218 - 207 = 11
|
| | | 0 | 2 | 6 | 9 | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | – | 2 | 0 | 7 | |
| | | | | 1 | 1 | |
|
STEP 16: BRING DOWN
|
| | | 0 | 2 | 6 | 9 | |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | – | 2 | 0 | 7 | |
| | | | | 1 | 1 | 2 |
STEP 17: DIVIDE 112 : 23 = 4 with a remainder of 20
|
| | | 0 | 2 | 6 | 9 | 4 |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | – | 2 | 0 | 7 | |
| | | | | 1 | 1 | 2 |
STEP 18: MULTIPLY 4 · 23 = 92
|
| | | 0 | 2 | 6 | 9 | 4 |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | – | 2 | 0 | 7 | |
| | | | | 1 | 1 | 2 |
| | | | | | 9 | 2 |
STEP 19: SUBTRACT 112 - 92 = 20
|
| | | 0 | 2 | 6 | 9 | 4 |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | – | 2 | 0 | 7 | |
| | | | | 1 | 1 | 2 |
| | | | | – | 9 | 2 |
| | | | | | 2 | 0 |
STEP 19: SUBTRACT 112 - 92 = 20
|
| | | 0 | 2 | 6 | 9 | 4 |
| 2 | 3 | 6 | 1 | 9 | 8 | 2 |
| | – | 0 | | | | |
| | | 6 | 1 | | | |
| | – | 4 | 6 | | | |
| | | 1 | 5 | 9 | | |
| | – | 1 | 3 | 8 | | |
| | | | 2 | 1 | 8 | |
| | | – | 2 | 0 | 7 | |
| | | | | 1 | 1 | 2 |
| | | | | – | 9 | 2 |
| | | | | | 2 | 0 |
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