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Question
What is the quotient and remainder when $ 44368 $ is divided by $ 23 $ ?
Answer
The quotient is 1929 and the remainder is 1.
Explanation
|
Division Table
|
| | | 0 | 1 | 9 | 2 | 9 |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | – | 4 | 6 | |
| | | | | 2 | 0 | 8 |
| | | | – | 2 | 0 | 7 |
| | | | | | | 1 |
STEP 0: set up a division table
|
| | | | | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
STEP 1: DIVIDE 4 : 23 = 0 with a remainder of 4
|
| | | 0 | | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
STEP 2: MULTIPLY 0 · 23 = 0
|
| | | 0 | | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | | 0 | | | | |
STEP 3: SUBTRACT 4 - 0 = 4
|
| | | 0 | | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
STEP 5: DIVIDE 44 : 23 = 1 with a remainder of 21
|
| | | 0 | 1 | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
STEP 6: MULTIPLY 1 · 23 = 23
|
| | | 0 | 1 | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | | 2 | 3 | | | |
STEP 7: SUBTRACT 44 - 23 = 21
|
| | | 0 | 1 | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
STEP 9: DIVIDE 213 : 23 = 9 with a remainder of 6
|
| | | 0 | 1 | 9 | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
STEP 10: MULTIPLY 9 · 23 = 207
|
| | | 0 | 1 | 9 | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | | 2 | 0 | 7 | | |
STEP 11: SUBTRACT 213 - 207 = 6
|
| | | 0 | 1 | 9 | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 9 | | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
STEP 13: DIVIDE 66 : 23 = 2 with a remainder of 20
|
| | | 0 | 1 | 9 | 2 | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
STEP 14: MULTIPLY 2 · 23 = 46
|
| | | 0 | 1 | 9 | 2 | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | | 4 | 6 | |
STEP 15: SUBTRACT 66 - 46 = 20
|
| | | 0 | 1 | 9 | 2 | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | – | 4 | 6 | |
| | | | | 2 | 0 | |
|
STEP 16: BRING DOWN
|
| | | 0 | 1 | 9 | 2 | |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | – | 4 | 6 | |
| | | | | 2 | 0 | 8 |
STEP 17: DIVIDE 208 : 23 = 9 with a remainder of 1
|
| | | 0 | 1 | 9 | 2 | 9 |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | – | 4 | 6 | |
| | | | | 2 | 0 | 8 |
STEP 18: MULTIPLY 9 · 23 = 207
|
| | | 0 | 1 | 9 | 2 | 9 |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | – | 4 | 6 | |
| | | | | 2 | 0 | 8 |
| | | | | 2 | 0 | 7 |
STEP 19: SUBTRACT 208 - 207 = 1
|
| | | 0 | 1 | 9 | 2 | 9 |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | – | 4 | 6 | |
| | | | | 2 | 0 | 8 |
| | | | – | 2 | 0 | 7 |
| | | | | | | 1 |
STEP 19: SUBTRACT 208 - 207 = 1
|
| | | 0 | 1 | 9 | 2 | 9 |
| 2 | 3 | 4 | 4 | 3 | 6 | 8 |
| | – | 0 | | | | |
| | | 4 | 4 | | | |
| | – | 2 | 3 | | | |
| | | 2 | 1 | 3 | | |
| | – | 2 | 0 | 7 | | |
| | | | | 6 | 6 | |
| | | | – | 4 | 6 | |
| | | | | 2 | 0 | 8 |
| | | | – | 2 | 0 | 7 |
| | | | | | | 1 |
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