Question
What is the quotient and remainder when $ 34411 $ is divided by $ 77 $ ?
Answer
The quotient is 446 and the remainder is 69.
Explanation
| Division Table | ||||||
| 0 | 0 | 4 | 4 | 6 | ||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| – | 3 | 0 | 8 | |||
| 5 | 3 | 1 | ||||
| – | 4 | 6 | 2 | |||
| 6 | 9 | |||||
|
STEP 0: set up a division table |
||||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
|
STEP 1: DIVIDE 3 : 77 = 0 with a remainder of 3 |
||||||
| 0 | ||||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
|
STEP 2: MULTIPLY 0 · 77 = 0 |
||||||
| 0 | ||||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| 0 | ||||||
|
STEP 3: SUBTRACT 3 - 0 = 3 |
||||||
| 0 | ||||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | ||||||
| STEP 4: BRING DOWN | ||||||
| 0 | ||||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
|
STEP 5: DIVIDE 34 : 77 = 0 with a remainder of 34 |
||||||
| 0 | 0 | |||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
|
STEP 6: MULTIPLY 0 · 77 = 0 |
||||||
| 0 | 0 | |||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| 0 | ||||||
|
STEP 7: SUBTRACT 34 - 0 = 34 |
||||||
| 0 | 0 | |||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | |||||
| STEP 8: BRING DOWN | ||||||
| 0 | 0 | |||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
|
STEP 9: DIVIDE 344 : 77 = 4 with a remainder of 36 |
||||||
| 0 | 0 | 4 | ||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
|
STEP 10: MULTIPLY 4 · 77 = 308 |
||||||
| 0 | 0 | 4 | ||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| 3 | 0 | 8 | ||||
|
STEP 11: SUBTRACT 344 - 308 = 36 |
||||||
| 0 | 0 | 4 | ||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | |||||
| STEP 12: BRING DOWN | ||||||
| 0 | 0 | 4 | ||||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
|
STEP 13: DIVIDE 361 : 77 = 4 with a remainder of 53 |
||||||
| 0 | 0 | 4 | 4 | |||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
|
STEP 14: MULTIPLY 4 · 77 = 308 |
||||||
| 0 | 0 | 4 | 4 | |||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| 3 | 0 | 8 | ||||
|
STEP 15: SUBTRACT 361 - 308 = 53 |
||||||
| 0 | 0 | 4 | 4 | |||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| – | 3 | 0 | 8 | |||
| 5 | 3 | |||||
| STEP 16: BRING DOWN | ||||||
| 0 | 0 | 4 | 4 | |||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| – | 3 | 0 | 8 | |||
| 5 | 3 | 1 | ||||
|
STEP 17: DIVIDE 531 : 77 = 6 with a remainder of 69 |
||||||
| 0 | 0 | 4 | 4 | 6 | ||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| – | 3 | 0 | 8 | |||
| 5 | 3 | 1 | ||||
|
STEP 18: MULTIPLY 6 · 77 = 462 |
||||||
| 0 | 0 | 4 | 4 | 6 | ||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| – | 3 | 0 | 8 | |||
| 5 | 3 | 1 | ||||
| 4 | 6 | 2 | ||||
|
STEP 19: SUBTRACT 531 - 462 = 69 |
||||||
| 0 | 0 | 4 | 4 | 6 | ||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| – | 3 | 0 | 8 | |||
| 5 | 3 | 1 | ||||
| – | 4 | 6 | 2 | |||
| 6 | 9 | |||||
|
STEP 19: SUBTRACT 531 - 462 = 69 |
||||||
| 0 | 0 | 4 | 4 | 6 | ||
| 7 | 7 | 3 | 4 | 4 | 1 | 1 |
| – | 0 | |||||
| 3 | 4 | |||||
| – | 0 | |||||
| 3 | 4 | 4 | ||||
| – | 3 | 0 | 8 | |||
| 3 | 6 | 1 | ||||
| – | 3 | 0 | 8 | |||
| 5 | 3 | 1 | ||||
| – | 4 | 6 | 2 | |||
| 6 | 9 | |||||
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