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Question
What is the quotient and remainder when $ 45206 $ is divided by $ 6 $ ?
Answer
The quotient is 7534 and the remainder is 2.
Explanation
|
Division Table
|
| | 0 | 7 | 5 | 3 | 4 |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | – | 1 | 8 | |
| | | | | 2 | 6 |
| | | | – | 2 | 4 |
| | | | | | 2 |
STEP 0: set up a division table
|
| | | | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
STEP 1: DIVIDE 4 : 6 = 0 with a remainder of 4
|
| | 0 | | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
STEP 2: MULTIPLY 0 · 6 = 0
|
| | 0 | | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| | 0 | | | | |
STEP 3: SUBTRACT 4 - 0 = 4
|
| | 0 | | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | | | | |
|
STEP 4: BRING DOWN
|
| | 0 | | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
STEP 5: DIVIDE 45 : 6 = 7 with a remainder of 3
|
| | 0 | 7 | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
STEP 6: MULTIPLY 7 · 6 = 42
|
| | 0 | 7 | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| | 4 | 2 | | | |
STEP 7: SUBTRACT 45 - 42 = 3
|
| | 0 | 7 | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | | | |
|
STEP 8: BRING DOWN
|
| | 0 | 7 | | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
STEP 9: DIVIDE 32 : 6 = 5 with a remainder of 2
|
| | 0 | 7 | 5 | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
STEP 10: MULTIPLY 5 · 6 = 30
|
| | 0 | 7 | 5 | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | | 3 | 0 | | |
STEP 11: SUBTRACT 32 - 30 = 2
|
| | 0 | 7 | 5 | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | | |
|
STEP 12: BRING DOWN
|
| | 0 | 7 | 5 | | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
STEP 13: DIVIDE 20 : 6 = 3 with a remainder of 2
|
| | 0 | 7 | 5 | 3 | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
STEP 14: MULTIPLY 3 · 6 = 18
|
| | 0 | 7 | 5 | 3 | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | | 1 | 8 | |
STEP 15: SUBTRACT 20 - 18 = 2
|
| | 0 | 7 | 5 | 3 | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | – | 1 | 8 | |
| | | | | 2 | |
|
STEP 16: BRING DOWN
|
| | 0 | 7 | 5 | 3 | |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | – | 1 | 8 | |
| | | | | 2 | 6 |
STEP 17: DIVIDE 26 : 6 = 4 with a remainder of 2
|
| | 0 | 7 | 5 | 3 | 4 |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | – | 1 | 8 | |
| | | | | 2 | 6 |
STEP 18: MULTIPLY 4 · 6 = 24
|
| | 0 | 7 | 5 | 3 | 4 |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | – | 1 | 8 | |
| | | | | 2 | 6 |
| | | | | 2 | 4 |
STEP 19: SUBTRACT 26 - 24 = 2
|
| | 0 | 7 | 5 | 3 | 4 |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | – | 1 | 8 | |
| | | | | 2 | 6 |
| | | | – | 2 | 4 |
| | | | | | 2 |
STEP 19: SUBTRACT 26 - 24 = 2
|
| | 0 | 7 | 5 | 3 | 4 |
| 6 | 4 | 5 | 2 | 0 | 6 |
| – | 0 | | | | |
| | 4 | 5 | | | |
| – | 4 | 2 | | | |
| | | 3 | 2 | | |
| | – | 3 | 0 | | |
| | | | 2 | 0 | |
| | | – | 1 | 8 | |
| | | | | 2 | 6 |
| | | | – | 2 | 4 |
| | | | | | 2 |
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