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What is the quotient and remainder when $ 2345 $ is divided by $ 310 $ ?
Answer
The quotient is 7 and the remainder is 175.
Explanation
Division Table
|
| | | 0 | 0 | 0 | 7 |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | – | 0 | |
| | | 2 | 3 | 4 | 5 |
| | – | 2 | 1 | 7 | 0 |
| | | | 1 | 7 | 5 |
STEP 0: set up a division table
|
| | | | | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
STEP 1: DIVIDE 2 : 310 = 0 with a remainder of 2
|
| | | 0 | | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
STEP 2: MULTIPLY 0 · 310 = 0
|
| | | 0 | | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | | | |
STEP 4: BRING DOWN
|
| | | 0 | | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
STEP 5: DIVIDE 23 : 310 = 0 with a remainder of 23
|
| | | 0 | 0 | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
STEP 6: MULTIPLY 0 · 310 = 0
|
| | | 0 | 0 | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 23 - 0 = 23
|
| | | 0 | 0 | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | | |
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
STEP 9: DIVIDE 234 : 310 = 0 with a remainder of 234
|
| | | 0 | 0 | 0 | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
STEP 10: MULTIPLY 0 · 310 = 0
|
| | | 0 | 0 | 0 | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | | 0 | |
STEP 11: SUBTRACT 234 - 0 = 234
|
| | | 0 | 0 | 0 | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | – | 0 | |
| | | 2 | 3 | 4 | |
STEP 12: BRING DOWN
|
| | | 0 | 0 | 0 | |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | – | 0 | |
| | | 2 | 3 | 4 | 5 |
STEP 13: DIVIDE 2345 : 310 = 7 with a remainder of 175
|
| | | 0 | 0 | 0 | 7 |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | – | 0 | |
| | | 2 | 3 | 4 | 5 |
STEP 14: MULTIPLY 7 · 310 = 2170
|
| | | 0 | 0 | 0 | 7 |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | – | 0 | |
| | | 2 | 3 | 4 | 5 |
| | | 2 | 1 | 7 | 0 |
STEP 15: SUBTRACT 2345 - 2170 = 175
|
| | | 0 | 0 | 0 | 7 |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | – | 0 | |
| | | 2 | 3 | 4 | 5 |
| | – | 2 | 1 | 7 | 0 |
| | | | 1 | 7 | 5 |
STEP 15: SUBTRACT 2345 - 2170 = 175
|
| | | 0 | 0 | 0 | 7 |
3 | 1 | 0 | 2 | 3 | 4 | 5 |
| | – | 0 | | | |
| | | 2 | 3 | | |
| | | – | 0 | | |
| | | 2 | 3 | 4 | |
| | | | – | 0 | |
| | | 2 | 3 | 4 | 5 |
| | – | 2 | 1 | 7 | 0 |
| | | | 1 | 7 | 5 |
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