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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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