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Question
What is the quotient and remainder when $ 35744 $ is divided by $ 13 $ ?
Answer
The quotient is 2749 and the remainder is 7.
Explanation
|
Division Table
|
| | | 0 | 2 | 7 | 4 | 9 |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 2 | 4 |
| | | | – | 1 | 1 | 7 |
| | | | | | | 7 |
STEP 0: set up a division table
|
| | | | | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
STEP 1: DIVIDE 3 : 13 = 0 with a remainder of 3
|
| | | 0 | | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
STEP 2: MULTIPLY 0 · 13 = 0
|
| | | 0 | | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | | 0 | | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
STEP 5: DIVIDE 35 : 13 = 2 with a remainder of 9
|
| | | 0 | 2 | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
STEP 6: MULTIPLY 2 · 13 = 26
|
| | | 0 | 2 | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | | 2 | 6 | | | |
STEP 7: SUBTRACT 35 - 26 = 9
|
| | | 0 | 2 | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
STEP 9: DIVIDE 97 : 13 = 7 with a remainder of 6
|
| | | 0 | 2 | 7 | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
STEP 10: MULTIPLY 7 · 13 = 91
|
| | | 0 | 2 | 7 | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | | 9 | 1 | | |
STEP 11: SUBTRACT 97 - 91 = 6
|
| | | 0 | 2 | 7 | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 7 | | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
STEP 13: DIVIDE 64 : 13 = 4 with a remainder of 12
|
| | | 0 | 2 | 7 | 4 | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
STEP 14: MULTIPLY 4 · 13 = 52
|
| | | 0 | 2 | 7 | 4 | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | | 5 | 2 | |
STEP 15: SUBTRACT 64 - 52 = 12
|
| | | 0 | 2 | 7 | 4 | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 2 | |
|
STEP 16: BRING DOWN
|
| | | 0 | 2 | 7 | 4 | |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 2 | 4 |
STEP 17: DIVIDE 124 : 13 = 9 with a remainder of 7
|
| | | 0 | 2 | 7 | 4 | 9 |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 2 | 4 |
STEP 18: MULTIPLY 9 · 13 = 117
|
| | | 0 | 2 | 7 | 4 | 9 |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 2 | 4 |
| | | | | 1 | 1 | 7 |
STEP 19: SUBTRACT 124 - 117 = 7
|
| | | 0 | 2 | 7 | 4 | 9 |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 2 | 4 |
| | | | – | 1 | 1 | 7 |
| | | | | | | 7 |
STEP 19: SUBTRACT 124 - 117 = 7
|
| | | 0 | 2 | 7 | 4 | 9 |
| 1 | 3 | 3 | 5 | 7 | 4 | 4 |
| | – | 0 | | | | |
| | | 3 | 5 | | | |
| | – | 2 | 6 | | | |
| | | | 9 | 7 | | |
| | | – | 9 | 1 | | |
| | | | | 6 | 4 | |
| | | | – | 5 | 2 | |
| | | | | 1 | 2 | 4 |
| | | | – | 1 | 1 | 7 |
| | | | | | | 7 |
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