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Question
What is the quotient and remainder when $ 19125 $ is divided by $ 3 $ ?
Answer
The quotient is 6375 and the remainder is 0.
Explanation
|
Division Table
|
| | 0 | 6 | 3 | 7 | 5 |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | – | 2 | 1 | |
| | | | | 1 | 5 |
| | | | – | 1 | 5 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
STEP 1: DIVIDE 1 : 3 = 0 with a remainder of 1
|
| | 0 | | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
STEP 2: MULTIPLY 0 · 3 = 0
|
| | 0 | | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| | 0 | | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | 0 | | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | | | | |
|
STEP 4: BRING DOWN
|
| | 0 | | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
STEP 5: DIVIDE 19 : 3 = 6 with a remainder of 1
|
| | 0 | 6 | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
STEP 6: MULTIPLY 6 · 3 = 18
|
| | 0 | 6 | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| | 1 | 8 | | | |
STEP 7: SUBTRACT 19 - 18 = 1
|
| | 0 | 6 | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | | | |
|
STEP 8: BRING DOWN
|
| | 0 | 6 | | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
STEP 9: DIVIDE 11 : 3 = 3 with a remainder of 2
|
| | 0 | 6 | 3 | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
STEP 10: MULTIPLY 3 · 3 = 9
|
| | 0 | 6 | 3 | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | | 9 | | |
STEP 11: SUBTRACT 11 - 9 = 2
|
| | 0 | 6 | 3 | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | | |
|
STEP 12: BRING DOWN
|
| | 0 | 6 | 3 | | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
STEP 13: DIVIDE 22 : 3 = 7 with a remainder of 1
|
| | 0 | 6 | 3 | 7 | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
STEP 14: MULTIPLY 7 · 3 = 21
|
| | 0 | 6 | 3 | 7 | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | | 2 | 1 | |
STEP 15: SUBTRACT 22 - 21 = 1
|
| | 0 | 6 | 3 | 7 | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | – | 2 | 1 | |
| | | | | 1 | |
|
STEP 16: BRING DOWN
|
| | 0 | 6 | 3 | 7 | |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | – | 2 | 1 | |
| | | | | 1 | 5 |
STEP 17: DIVIDE 15 : 3 = 5 with a remainder of 0
|
| | 0 | 6 | 3 | 7 | 5 |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | – | 2 | 1 | |
| | | | | 1 | 5 |
STEP 18: MULTIPLY 5 · 3 = 15
|
| | 0 | 6 | 3 | 7 | 5 |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | – | 2 | 1 | |
| | | | | 1 | 5 |
| | | | | 1 | 5 |
STEP 19: SUBTRACT 15 - 15 = 0
|
| | 0 | 6 | 3 | 7 | 5 |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | – | 2 | 1 | |
| | | | | 1 | 5 |
| | | | – | 1 | 5 |
| | | | | | 0 |
STEP 19: SUBTRACT 15 - 15 = 0
|
| | 0 | 6 | 3 | 7 | 5 |
| 3 | 1 | 9 | 1 | 2 | 5 |
| – | 0 | | | | |
| | 1 | 9 | | | |
| – | 1 | 8 | | | |
| | | 1 | 1 | | |
| | | – | 9 | | |
| | | | 2 | 2 | |
| | | – | 2 | 1 | |
| | | | | 1 | 5 |
| | | | – | 1 | 5 |
| | | | | | 0 |
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