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What is the quotient and remainder when $ 78384 $ is divided by $ 12 $ ?
Answer
The quotient is 6532 and the remainder is 0.
Explanation
Division Table
|
| | 0 | 6 | 5 | 3 | 2 |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | – | 3 | 6 | |
| | | | | 2 | 4 |
| | | | – | 2 | 4 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
STEP 1: DIVIDE 7 : 12 = 0 with a remainder of 7
|
| | 0 | | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
STEP 2: MULTIPLY 0 · 12 = 0
|
| | 0 | | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| | 0 | | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | 0 | | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | | | | |
STEP 4: BRING DOWN
|
| | 0 | | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
STEP 5: DIVIDE 78 : 12 = 6 with a remainder of 6
|
| | 0 | 6 | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
STEP 6: MULTIPLY 6 · 12 = 72
|
| | 0 | 6 | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| | 7 | 2 | | | |
STEP 7: SUBTRACT 78 - 72 = 6
|
| | 0 | 6 | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | | | |
STEP 8: BRING DOWN
|
| | 0 | 6 | | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
STEP 9: DIVIDE 63 : 12 = 5 with a remainder of 3
|
| | 0 | 6 | 5 | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
STEP 10: MULTIPLY 5 · 12 = 60
|
| | 0 | 6 | 5 | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | | 6 | 0 | | |
STEP 11: SUBTRACT 63 - 60 = 3
|
| | 0 | 6 | 5 | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | | |
STEP 12: BRING DOWN
|
| | 0 | 6 | 5 | | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
STEP 13: DIVIDE 38 : 12 = 3 with a remainder of 2
|
| | 0 | 6 | 5 | 3 | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
STEP 14: MULTIPLY 3 · 12 = 36
|
| | 0 | 6 | 5 | 3 | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | | 3 | 6 | |
STEP 15: SUBTRACT 38 - 36 = 2
|
| | 0 | 6 | 5 | 3 | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | – | 3 | 6 | |
| | | | | 2 | |
STEP 16: BRING DOWN
|
| | 0 | 6 | 5 | 3 | |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | – | 3 | 6 | |
| | | | | 2 | 4 |
STEP 17: DIVIDE 24 : 12 = 2 with a remainder of 0
|
| | 0 | 6 | 5 | 3 | 2 |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | – | 3 | 6 | |
| | | | | 2 | 4 |
STEP 18: MULTIPLY 2 · 12 = 24
|
| | 0 | 6 | 5 | 3 | 2 |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | – | 3 | 6 | |
| | | | | 2 | 4 |
| | | | | 2 | 4 |
STEP 19: SUBTRACT 24 - 24 = 0
|
| | 0 | 6 | 5 | 3 | 2 |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | – | 3 | 6 | |
| | | | | 2 | 4 |
| | | | – | 2 | 4 |
| | | | | | 0 |
STEP 19: SUBTRACT 24 - 24 = 0
|
| | 0 | 6 | 5 | 3 | 2 |
1 | 2 | 7 | 8 | 3 | 8 | 4 |
| – | 0 | | | | |
| | 7 | 8 | | | |
| – | 7 | 2 | | | |
| | | 6 | 3 | | |
| | – | 6 | 0 | | |
| | | | 3 | 8 | |
| | | – | 3 | 6 | |
| | | | | 2 | 4 |
| | | | – | 2 | 4 |
| | | | | | 0 |
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