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What is the quotient and remainder when $ 35152 $ is divided by $ 32 $ ?
Answer
The quotient is 1098 and the remainder is 16.
Explanation
Division Table
|
| | 0 | 1 | 0 | 9 | 8 |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | – | 2 | 8 | 8 | |
| | | | 2 | 7 | 2 |
| | | – | 2 | 5 | 6 |
| | | | | 1 | 6 |
STEP 0: set up a division table
|
| | | | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
STEP 1: DIVIDE 3 : 32 = 0 with a remainder of 3
|
| | 0 | | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
STEP 2: MULTIPLY 0 · 32 = 0
|
| | 0 | | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| | 0 | | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | 0 | | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | | | | |
STEP 4: BRING DOWN
|
| | 0 | | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
STEP 5: DIVIDE 35 : 32 = 1 with a remainder of 3
|
| | 0 | 1 | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
STEP 6: MULTIPLY 1 · 32 = 32
|
| | 0 | 1 | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| | 3 | 2 | | | |
STEP 7: SUBTRACT 35 - 32 = 3
|
| | 0 | 1 | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | | | |
STEP 8: BRING DOWN
|
| | 0 | 1 | | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
STEP 9: DIVIDE 31 : 32 = 0 with a remainder of 31
|
| | 0 | 1 | 0 | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
STEP 10: MULTIPLY 0 · 32 = 0
|
| | 0 | 1 | 0 | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | | 0 | | |
STEP 11: SUBTRACT 31 - 0 = 31
|
| | 0 | 1 | 0 | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | | |
STEP 12: BRING DOWN
|
| | 0 | 1 | 0 | | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
STEP 13: DIVIDE 315 : 32 = 9 with a remainder of 27
|
| | 0 | 1 | 0 | 9 | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
STEP 14: MULTIPLY 9 · 32 = 288
|
| | 0 | 1 | 0 | 9 | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | | 2 | 8 | 8 | |
STEP 15: SUBTRACT 315 - 288 = 27
|
| | 0 | 1 | 0 | 9 | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | – | 2 | 8 | 8 | |
| | | | 2 | 7 | |
STEP 16: BRING DOWN
|
| | 0 | 1 | 0 | 9 | |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | – | 2 | 8 | 8 | |
| | | | 2 | 7 | 2 |
STEP 17: DIVIDE 272 : 32 = 8 with a remainder of 16
|
| | 0 | 1 | 0 | 9 | 8 |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | – | 2 | 8 | 8 | |
| | | | 2 | 7 | 2 |
STEP 18: MULTIPLY 8 · 32 = 256
|
| | 0 | 1 | 0 | 9 | 8 |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | – | 2 | 8 | 8 | |
| | | | 2 | 7 | 2 |
| | | | 2 | 5 | 6 |
STEP 19: SUBTRACT 272 - 256 = 16
|
| | 0 | 1 | 0 | 9 | 8 |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | – | 2 | 8 | 8 | |
| | | | 2 | 7 | 2 |
| | | – | 2 | 5 | 6 |
| | | | | 1 | 6 |
STEP 19: SUBTRACT 272 - 256 = 16
|
| | 0 | 1 | 0 | 9 | 8 |
3 | 2 | 3 | 5 | 1 | 5 | 2 |
| – | 0 | | | | |
| | 3 | 5 | | | |
| – | 3 | 2 | | | |
| | | 3 | 1 | | |
| | | – | 0 | | |
| | | 3 | 1 | 5 | |
| | – | 2 | 8 | 8 | |
| | | | 2 | 7 | 2 |
| | | – | 2 | 5 | 6 |
| | | | | 1 | 6 |
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