Question
What is the quotient and remainder when $ 770 $ is divided by $ 13 $ ?
Answer
The quotient is 59 and the remainder is 3.
Explanation
| Division Table | ||||
| 0 | 5 | 9 | ||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| – | 6 | 5 | ||
| 1 | 2 | 0 | ||
| – | 1 | 1 | 7 | |
| 3 | ||||
|
STEP 0: set up a division table |
||||
| 1 | 3 | 7 | 7 | 0 |
|
STEP 1: DIVIDE 7 : 13 = 0 with a remainder of 7 |
||||
| 0 | ||||
| 1 | 3 | 7 | 7 | 0 |
|
STEP 2: MULTIPLY 0 · 13 = 0 |
||||
| 0 | ||||
| 1 | 3 | 7 | 7 | 0 |
| 0 | ||||
|
STEP 3: SUBTRACT 7 - 0 = 7 |
||||
| 0 | ||||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | ||||
| STEP 4: BRING DOWN | ||||
| 0 | ||||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
|
STEP 5: DIVIDE 77 : 13 = 5 with a remainder of 12 |
||||
| 0 | 5 | |||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
|
STEP 6: MULTIPLY 5 · 13 = 65 |
||||
| 0 | 5 | |||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| 6 | 5 | |||
|
STEP 7: SUBTRACT 77 - 65 = 12 |
||||
| 0 | 5 | |||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| – | 6 | 5 | ||
| 1 | 2 | |||
| STEP 8: BRING DOWN | ||||
| 0 | 5 | |||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| – | 6 | 5 | ||
| 1 | 2 | 0 | ||
|
STEP 9: DIVIDE 120 : 13 = 9 with a remainder of 3 |
||||
| 0 | 5 | 9 | ||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| – | 6 | 5 | ||
| 1 | 2 | 0 | ||
|
STEP 10: MULTIPLY 9 · 13 = 117 |
||||
| 0 | 5 | 9 | ||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| – | 6 | 5 | ||
| 1 | 2 | 0 | ||
| 1 | 1 | 7 | ||
|
STEP 11: SUBTRACT 120 - 117 = 3 |
||||
| 0 | 5 | 9 | ||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| – | 6 | 5 | ||
| 1 | 2 | 0 | ||
| – | 1 | 1 | 7 | |
| 3 | ||||
|
STEP 11: SUBTRACT 120 - 117 = 3 |
||||
| 0 | 5 | 9 | ||
| 1 | 3 | 7 | 7 | 0 |
| – | 0 | |||
| 7 | 7 | |||
| – | 6 | 5 | ||
| 1 | 2 | 0 | ||
| – | 1 | 1 | 7 | |
| 3 | ||||
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