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Question
What is the quotient and remainder when $ 675420 $ is divided by $ 15 $ ?
Answer
The quotient is 45028 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 4 | 5 | 0 | 2 | 8 |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | – | 3 | 0 | | |
| | | | | 1 | 2 | 0 | |
| | | | – | 1 | 2 | 0 | |
| | | | | | | 0 | |
STEP 0: set up a division table
|
| | | | | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
STEP 1: DIVIDE 6 : 15 = 0 with a remainder of 6
|
| | | 0 | | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
STEP 2: MULTIPLY 0 · 15 = 0
|
| | | 0 | | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | | 0 | | | | | |
STEP 3: SUBTRACT 6 - 0 = 6
|
| | | 0 | | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
STEP 5: DIVIDE 67 : 15 = 4 with a remainder of 7
|
| | | 0 | 4 | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
STEP 6: MULTIPLY 4 · 15 = 60
|
| | | 0 | 4 | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | | 6 | 0 | | | | |
STEP 7: SUBTRACT 67 - 60 = 7
|
| | | 0 | 4 | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 4 | | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
STEP 9: DIVIDE 75 : 15 = 5 with a remainder of 0
|
| | | 0 | 4 | 5 | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
STEP 10: MULTIPLY 5 · 15 = 75
|
| | | 0 | 4 | 5 | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | | 7 | 5 | | | |
STEP 11: SUBTRACT 75 - 75 = 0
|
| | | 0 | 4 | 5 | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 0 | | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 4 | 5 | | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
STEP 13: DIVIDE 4 : 15 = 0 with a remainder of 4
|
| | | 0 | 4 | 5 | 0 | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
STEP 14: MULTIPLY 0 · 15 = 0
|
| | | 0 | 4 | 5 | 0 | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | | 0 | | | |
STEP 15: SUBTRACT 4 - 0 = 4
|
| | | 0 | 4 | 5 | 0 | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | | | |
|
STEP 16: BRING DOWN
|
| | | 0 | 4 | 5 | 0 | | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
STEP 17: DIVIDE 42 : 15 = 2 with a remainder of 12
|
| | | 0 | 4 | 5 | 0 | 2 | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
STEP 18: MULTIPLY 2 · 15 = 30
|
| | | 0 | 4 | 5 | 0 | 2 | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | | 3 | 0 | | |
STEP 19: SUBTRACT 42 - 30 = 12
|
| | | 0 | 4 | 5 | 0 | 2 | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | – | 3 | 0 | | |
| | | | | 1 | 2 | | |
|
STEP 20: BRING DOWN
|
| | | 0 | 4 | 5 | 0 | 2 | |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | – | 3 | 0 | | |
| | | | | 1 | 2 | 0 | |
STEP 21: DIVIDE 120 : 15 = 8 with a remainder of 0
|
| | | 0 | 4 | 5 | 0 | 2 | 8 |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | – | 3 | 0 | | |
| | | | | 1 | 2 | 0 | |
STEP 22: MULTIPLY 8 · 15 = 120
|
| | | 0 | 4 | 5 | 0 | 2 | 8 |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | – | 3 | 0 | | |
| | | | | 1 | 2 | 0 | |
| | | | | 1 | 2 | 0 | |
STEP 23: SUBTRACT 120 - 120 = 0
|
| | | 0 | 4 | 5 | 0 | 2 | 8 |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | – | 3 | 0 | | |
| | | | | 1 | 2 | 0 | |
| | | | – | 1 | 2 | 0 | |
| | | | | | | 0 | |
STEP 23: SUBTRACT 120 - 120 = 0
|
| | | 0 | 4 | 5 | 0 | 2 | 8 |
| 1 | 5 | 6 | 7 | 5 | 4 | 2 | 0 |
| | – | 0 | | | | | |
| | | 6 | 7 | | | | |
| | – | 6 | 0 | | | | |
| | | | 7 | 5 | | | |
| | | – | 7 | 5 | | | |
| | | | | 4 | | | |
| | | | – | 0 | | | |
| | | | | 4 | 2 | | |
| | | | – | 3 | 0 | | |
| | | | | 1 | 2 | 0 | |
| | | | – | 1 | 2 | 0 | |
| | | | | | | 0 | |
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