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Question
What is the quotient and remainder when $ 1230 $ is divided by $ 73 $ ?
Answer
The quotient is 16 and the remainder is 62.
Explanation
|
Division Table
|
| | | 0 | 0 | 1 | 6 |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | – | 7 | 3 | |
| | | | 5 | 0 | 0 |
| | | – | 4 | 3 | 8 |
| | | | | 6 | 2 |
STEP 0: set up a division table
|
| | | | | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
STEP 1: DIVIDE 1 : 73 = 0 with a remainder of 1
|
| | | 0 | | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
STEP 2: MULTIPLY 0 · 73 = 0
|
| | | 0 | | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | | 0 | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | | 0 | | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
STEP 5: DIVIDE 12 : 73 = 0 with a remainder of 12
|
| | | 0 | 0 | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
STEP 6: MULTIPLY 0 · 73 = 0
|
| | | 0 | 0 | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 12 - 0 = 12
|
| | | 0 | 0 | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
STEP 9: DIVIDE 123 : 73 = 1 with a remainder of 50
|
| | | 0 | 0 | 1 | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
STEP 10: MULTIPLY 1 · 73 = 73
|
| | | 0 | 0 | 1 | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | | 7 | 3 | |
STEP 11: SUBTRACT 123 - 73 = 50
|
| | | 0 | 0 | 1 | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | – | 7 | 3 | |
| | | | 5 | 0 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 0 | 1 | |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | – | 7 | 3 | |
| | | | 5 | 0 | 0 |
STEP 13: DIVIDE 500 : 73 = 6 with a remainder of 62
|
| | | 0 | 0 | 1 | 6 |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | – | 7 | 3 | |
| | | | 5 | 0 | 0 |
STEP 14: MULTIPLY 6 · 73 = 438
|
| | | 0 | 0 | 1 | 6 |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | – | 7 | 3 | |
| | | | 5 | 0 | 0 |
| | | | 4 | 3 | 8 |
STEP 15: SUBTRACT 500 - 438 = 62
|
| | | 0 | 0 | 1 | 6 |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | – | 7 | 3 | |
| | | | 5 | 0 | 0 |
| | | – | 4 | 3 | 8 |
| | | | | 6 | 2 |
STEP 15: SUBTRACT 500 - 438 = 62
|
| | | 0 | 0 | 1 | 6 |
| 7 | 3 | 1 | 2 | 3 | 0 |
| | – | 0 | | | |
| | | 1 | 2 | | |
| | | – | 0 | | |
| | | 1 | 2 | 3 | |
| | | – | 7 | 3 | |
| | | | 5 | 0 | 0 |
| | | – | 4 | 3 | 8 |
| | | | | 6 | 2 |
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