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What is the quotient and remainder when $ 336752 $ is divided by $ 31 $ ?
Answer
The quotient is 10862 and the remainder is 30.
Explanation
Division Table
|
| | 0 | 1 | 0 | 8 | 6 | 2 |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | – | 1 | 8 | 6 | |
| | | | | | 9 | 2 |
| | | | | – | 6 | 2 |
| | | | | | 3 | 0 |
STEP 0: set up a division table
|
| | | | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
STEP 1: DIVIDE 3 : 31 = 0 with a remainder of 3
|
| | 0 | | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
STEP 2: MULTIPLY 0 · 31 = 0
|
| | 0 | | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| | 0 | | | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | 0 | | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | | | | | |
STEP 4: BRING DOWN
|
| | 0 | | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
STEP 5: DIVIDE 33 : 31 = 1 with a remainder of 2
|
| | 0 | 1 | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
STEP 6: MULTIPLY 1 · 31 = 31
|
| | 0 | 1 | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| | 3 | 1 | | | | |
STEP 7: SUBTRACT 33 - 31 = 2
|
| | 0 | 1 | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | | | | |
STEP 8: BRING DOWN
|
| | 0 | 1 | | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
STEP 9: DIVIDE 26 : 31 = 0 with a remainder of 26
|
| | 0 | 1 | 0 | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
STEP 10: MULTIPLY 0 · 31 = 0
|
| | 0 | 1 | 0 | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | | 0 | | | |
STEP 11: SUBTRACT 26 - 0 = 26
|
| | 0 | 1 | 0 | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | | | |
STEP 12: BRING DOWN
|
| | 0 | 1 | 0 | | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
STEP 13: DIVIDE 267 : 31 = 8 with a remainder of 19
|
| | 0 | 1 | 0 | 8 | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
STEP 14: MULTIPLY 8 · 31 = 248
|
| | 0 | 1 | 0 | 8 | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | | 2 | 4 | 8 | | |
STEP 15: SUBTRACT 267 - 248 = 19
|
| | 0 | 1 | 0 | 8 | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | | |
STEP 16: BRING DOWN
|
| | 0 | 1 | 0 | 8 | | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
STEP 17: DIVIDE 195 : 31 = 6 with a remainder of 9
|
| | 0 | 1 | 0 | 8 | 6 | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
STEP 18: MULTIPLY 6 · 31 = 186
|
| | 0 | 1 | 0 | 8 | 6 | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | | 1 | 8 | 6 | |
STEP 19: SUBTRACT 195 - 186 = 9
|
| | 0 | 1 | 0 | 8 | 6 | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | – | 1 | 8 | 6 | |
| | | | | | 9 | |
STEP 20: BRING DOWN
|
| | 0 | 1 | 0 | 8 | 6 | |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | – | 1 | 8 | 6 | |
| | | | | | 9 | 2 |
STEP 21: DIVIDE 92 : 31 = 2 with a remainder of 30
|
| | 0 | 1 | 0 | 8 | 6 | 2 |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | – | 1 | 8 | 6 | |
| | | | | | 9 | 2 |
STEP 22: MULTIPLY 2 · 31 = 62
|
| | 0 | 1 | 0 | 8 | 6 | 2 |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | – | 1 | 8 | 6 | |
| | | | | | 9 | 2 |
| | | | | | 6 | 2 |
STEP 23: SUBTRACT 92 - 62 = 30
|
| | 0 | 1 | 0 | 8 | 6 | 2 |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | – | 1 | 8 | 6 | |
| | | | | | 9 | 2 |
| | | | | – | 6 | 2 |
| | | | | | 3 | 0 |
STEP 23: SUBTRACT 92 - 62 = 30
|
| | 0 | 1 | 0 | 8 | 6 | 2 |
3 | 1 | 3 | 3 | 6 | 7 | 5 | 2 |
| – | 0 | | | | | |
| | 3 | 3 | | | | |
| – | 3 | 1 | | | | |
| | | 2 | 6 | | | |
| | | – | 0 | | | |
| | | 2 | 6 | 7 | | |
| | – | 2 | 4 | 8 | | |
| | | | 1 | 9 | 5 | |
| | | – | 1 | 8 | 6 | |
| | | | | | 9 | 2 |
| | | | | – | 6 | 2 |
| | | | | | 3 | 0 |
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