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Question
What is the quotient and remainder when $ 71698 $ is divided by $ 13 $ ?
Answer
The quotient is 5515 and the remainder is 3.
Explanation
|
Division Table
|
| | | 0 | 5 | 5 | 1 | 5 |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | – | 1 | 3 | |
| | | | | | 6 | 8 |
| | | | | – | 6 | 5 |
| | | | | | | 3 |
STEP 0: set up a division table
|
| | | | | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
STEP 1: DIVIDE 7 : 13 = 0 with a remainder of 7
|
| | | 0 | | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
STEP 2: MULTIPLY 0 · 13 = 0
|
| | | 0 | | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | | 0 | | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | | 0 | | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
STEP 5: DIVIDE 71 : 13 = 5 with a remainder of 6
|
| | | 0 | 5 | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
STEP 6: MULTIPLY 5 · 13 = 65
|
| | | 0 | 5 | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | | 6 | 5 | | | |
STEP 7: SUBTRACT 71 - 65 = 6
|
| | | 0 | 5 | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 5 | | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
STEP 9: DIVIDE 66 : 13 = 5 with a remainder of 1
|
| | | 0 | 5 | 5 | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
STEP 10: MULTIPLY 5 · 13 = 65
|
| | | 0 | 5 | 5 | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | | 6 | 5 | | |
STEP 11: SUBTRACT 66 - 65 = 1
|
| | | 0 | 5 | 5 | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 5 | 5 | | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
STEP 13: DIVIDE 19 : 13 = 1 with a remainder of 6
|
| | | 0 | 5 | 5 | 1 | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
STEP 14: MULTIPLY 1 · 13 = 13
|
| | | 0 | 5 | 5 | 1 | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | | 1 | 3 | |
STEP 15: SUBTRACT 19 - 13 = 6
|
| | | 0 | 5 | 5 | 1 | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | – | 1 | 3 | |
| | | | | | 6 | |
|
STEP 16: BRING DOWN
|
| | | 0 | 5 | 5 | 1 | |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | – | 1 | 3 | |
| | | | | | 6 | 8 |
STEP 17: DIVIDE 68 : 13 = 5 with a remainder of 3
|
| | | 0 | 5 | 5 | 1 | 5 |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | – | 1 | 3 | |
| | | | | | 6 | 8 |
STEP 18: MULTIPLY 5 · 13 = 65
|
| | | 0 | 5 | 5 | 1 | 5 |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | – | 1 | 3 | |
| | | | | | 6 | 8 |
| | | | | | 6 | 5 |
STEP 19: SUBTRACT 68 - 65 = 3
|
| | | 0 | 5 | 5 | 1 | 5 |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | – | 1 | 3 | |
| | | | | | 6 | 8 |
| | | | | – | 6 | 5 |
| | | | | | | 3 |
STEP 19: SUBTRACT 68 - 65 = 3
|
| | | 0 | 5 | 5 | 1 | 5 |
| 1 | 3 | 7 | 1 | 6 | 9 | 8 |
| | – | 0 | | | | |
| | | 7 | 1 | | | |
| | – | 6 | 5 | | | |
| | | | 6 | 6 | | |
| | | – | 6 | 5 | | |
| | | | | 1 | 9 | |
| | | | – | 1 | 3 | |
| | | | | | 6 | 8 |
| | | | | – | 6 | 5 |
| | | | | | | 3 |
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