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Question
What is the quotient and remainder when $ 1612 $ is divided by $ 13 $ ?
Answer
The quotient is 124 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 1 | 2 | 4 |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | – | 2 | 6 | |
| | | | | 5 | 2 |
| | | | – | 5 | 2 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
STEP 1: DIVIDE 1 : 13 = 0 with a remainder of 1
|
| | | 0 | | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
STEP 2: MULTIPLY 0 · 13 = 0
|
| | | 0 | | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | | 0 | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | | 0 | | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
STEP 5: DIVIDE 16 : 13 = 1 with a remainder of 3
|
| | | 0 | 1 | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
STEP 6: MULTIPLY 1 · 13 = 13
|
| | | 0 | 1 | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | | 1 | 3 | | |
STEP 7: SUBTRACT 16 - 13 = 3
|
| | | 0 | 1 | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
STEP 9: DIVIDE 31 : 13 = 2 with a remainder of 5
|
| | | 0 | 1 | 2 | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
STEP 10: MULTIPLY 2 · 13 = 26
|
| | | 0 | 1 | 2 | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | | 2 | 6 | |
STEP 11: SUBTRACT 31 - 26 = 5
|
| | | 0 | 1 | 2 | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | – | 2 | 6 | |
| | | | | 5 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 2 | |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | – | 2 | 6 | |
| | | | | 5 | 2 |
STEP 13: DIVIDE 52 : 13 = 4 with a remainder of 0
|
| | | 0 | 1 | 2 | 4 |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | – | 2 | 6 | |
| | | | | 5 | 2 |
STEP 14: MULTIPLY 4 · 13 = 52
|
| | | 0 | 1 | 2 | 4 |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | – | 2 | 6 | |
| | | | | 5 | 2 |
| | | | | 5 | 2 |
STEP 15: SUBTRACT 52 - 52 = 0
|
| | | 0 | 1 | 2 | 4 |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | – | 2 | 6 | |
| | | | | 5 | 2 |
| | | | – | 5 | 2 |
| | | | | | 0 |
STEP 15: SUBTRACT 52 - 52 = 0
|
| | | 0 | 1 | 2 | 4 |
| 1 | 3 | 1 | 6 | 1 | 2 |
| | – | 0 | | | |
| | | 1 | 6 | | |
| | – | 1 | 3 | | |
| | | | 3 | 1 | |
| | | – | 2 | 6 | |
| | | | | 5 | 2 |
| | | | – | 5 | 2 |
| | | | | | 0 |
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