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What is the quotient and remainder when $ 87212 $ is divided by $ 123 $ ?
Answer
The quotient is 709 and the remainder is 5.
Explanation
Division Table
|
| | | 0 | 0 | 7 | 0 | 9 |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | – | 0 | |
| | | | 1 | 1 | 1 | 2 |
| | | – | 1 | 1 | 0 | 7 |
| | | | | | | 5 |
STEP 0: set up a division table
|
| | | | | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
STEP 1: DIVIDE 8 : 123 = 0 with a remainder of 8
|
| | | 0 | | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
STEP 2: MULTIPLY 0 · 123 = 0
|
| | | 0 | | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | | 0 | | | | |
STEP 3: SUBTRACT 8 - 0 = 8
|
| | | 0 | | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | | | | |
STEP 4: BRING DOWN
|
| | | 0 | | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
STEP 5: DIVIDE 87 : 123 = 0 with a remainder of 87
|
| | | 0 | 0 | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
STEP 6: MULTIPLY 0 · 123 = 0
|
| | | 0 | 0 | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | | 0 | | | |
STEP 7: SUBTRACT 87 - 0 = 87
|
| | | 0 | 0 | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | | | |
STEP 8: BRING DOWN
|
| | | 0 | 0 | | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
STEP 9: DIVIDE 872 : 123 = 7 with a remainder of 11
|
| | | 0 | 0 | 7 | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
STEP 10: MULTIPLY 7 · 123 = 861
|
| | | 0 | 0 | 7 | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | | 8 | 6 | 1 | | |
STEP 11: SUBTRACT 872 - 861 = 11
|
| | | 0 | 0 | 7 | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | | |
STEP 12: BRING DOWN
|
| | | 0 | 0 | 7 | | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
STEP 13: DIVIDE 111 : 123 = 0 with a remainder of 111
|
| | | 0 | 0 | 7 | 0 | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
STEP 14: MULTIPLY 0 · 123 = 0
|
| | | 0 | 0 | 7 | 0 | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | | 0 | |
STEP 15: SUBTRACT 111 - 0 = 111
|
| | | 0 | 0 | 7 | 0 | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | – | 0 | |
| | | | 1 | 1 | 1 | |
STEP 16: BRING DOWN
|
| | | 0 | 0 | 7 | 0 | |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | – | 0 | |
| | | | 1 | 1 | 1 | 2 |
STEP 17: DIVIDE 1112 : 123 = 9 with a remainder of 5
|
| | | 0 | 0 | 7 | 0 | 9 |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | – | 0 | |
| | | | 1 | 1 | 1 | 2 |
STEP 18: MULTIPLY 9 · 123 = 1107
|
| | | 0 | 0 | 7 | 0 | 9 |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | – | 0 | |
| | | | 1 | 1 | 1 | 2 |
| | | | 1 | 1 | 0 | 7 |
STEP 19: SUBTRACT 1112 - 1107 = 5
|
| | | 0 | 0 | 7 | 0 | 9 |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | – | 0 | |
| | | | 1 | 1 | 1 | 2 |
| | | – | 1 | 1 | 0 | 7 |
| | | | | | | 5 |
STEP 19: SUBTRACT 1112 - 1107 = 5
|
| | | 0 | 0 | 7 | 0 | 9 |
1 | 2 | 3 | 8 | 7 | 2 | 1 | 2 |
| | – | 0 | | | | |
| | | 8 | 7 | | | |
| | | – | 0 | | | |
| | | 8 | 7 | 2 | | |
| | – | 8 | 6 | 1 | | |
| | | | 1 | 1 | 1 | |
| | | | | – | 0 | |
| | | | 1 | 1 | 1 | 2 |
| | | – | 1 | 1 | 0 | 7 |
| | | | | | | 5 |
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