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Question
What is the quotient and remainder when $ 6543 $ is divided by $ 32 $ ?
Answer
The quotient is 204 and the remainder is 15.
Explanation
Division Table
|
| | 0 | 2 | 0 | 4 |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | – | 0 | |
| | | 1 | 4 | 3 |
| | – | 1 | 2 | 8 |
| | | | 1 | 5 |
STEP 0: set up a division table
|
| | | | | |
3 | 2 | 6 | 5 | 4 | 3 |
STEP 1: DIVIDE 6 : 32 = 0 with a remainder of 6
|
| | 0 | | | |
3 | 2 | 6 | 5 | 4 | 3 |
STEP 2: MULTIPLY 0 · 32 = 0
|
| | 0 | | | |
3 | 2 | 6 | 5 | 4 | 3 |
| | 0 | | | |
STEP 3: SUBTRACT 6 - 0 = 6
|
| | 0 | | | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
STEP 5: DIVIDE 65 : 32 = 2 with a remainder of 1
|
| | 0 | 2 | | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
STEP 6: MULTIPLY 2 · 32 = 64
|
| | 0 | 2 | | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| | 6 | 4 | | |
STEP 7: SUBTRACT 65 - 64 = 1
|
| | 0 | 2 | | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | | |
STEP 8: BRING DOWN
|
| | 0 | 2 | | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
STEP 9: DIVIDE 14 : 32 = 0 with a remainder of 14
|
| | 0 | 2 | 0 | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
STEP 10: MULTIPLY 0 · 32 = 0
|
| | 0 | 2 | 0 | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | | 0 | |
STEP 11: SUBTRACT 14 - 0 = 14
|
| | 0 | 2 | 0 | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | – | 0 | |
| | | 1 | 4 | |
STEP 12: BRING DOWN
|
| | 0 | 2 | 0 | |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | – | 0 | |
| | | 1 | 4 | 3 |
STEP 13: DIVIDE 143 : 32 = 4 with a remainder of 15
|
| | 0 | 2 | 0 | 4 |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | – | 0 | |
| | | 1 | 4 | 3 |
STEP 14: MULTIPLY 4 · 32 = 128
|
| | 0 | 2 | 0 | 4 |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | – | 0 | |
| | | 1 | 4 | 3 |
| | | 1 | 2 | 8 |
STEP 15: SUBTRACT 143 - 128 = 15
|
| | 0 | 2 | 0 | 4 |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | – | 0 | |
| | | 1 | 4 | 3 |
| | – | 1 | 2 | 8 |
| | | | 1 | 5 |
STEP 15: SUBTRACT 143 - 128 = 15
|
| | 0 | 2 | 0 | 4 |
3 | 2 | 6 | 5 | 4 | 3 |
| – | 0 | | | |
| | 6 | 5 | | |
| – | 6 | 4 | | |
| | | 1 | 4 | |
| | | – | 0 | |
| | | 1 | 4 | 3 |
| | – | 1 | 2 | 8 |
| | | | 1 | 5 |
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