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Question
What is the quotient and remainder when $ 2048 $ is divided by $ 16 $ ?
Answer
The quotient is 128 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 1 | 2 | 8 |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | – | 3 | 2 | |
| | | | 1 | 2 | 8 |
| | | – | 1 | 2 | 8 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
STEP 1: DIVIDE 2 : 16 = 0 with a remainder of 2
|
| | | 0 | | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
STEP 2: MULTIPLY 0 · 16 = 0
|
| | | 0 | | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
STEP 5: DIVIDE 20 : 16 = 1 with a remainder of 4
|
| | | 0 | 1 | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
STEP 6: MULTIPLY 1 · 16 = 16
|
| | | 0 | 1 | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | | 1 | 6 | | |
STEP 7: SUBTRACT 20 - 16 = 4
|
| | | 0 | 1 | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
STEP 9: DIVIDE 44 : 16 = 2 with a remainder of 12
|
| | | 0 | 1 | 2 | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
STEP 10: MULTIPLY 2 · 16 = 32
|
| | | 0 | 1 | 2 | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | | 3 | 2 | |
STEP 11: SUBTRACT 44 - 32 = 12
|
| | | 0 | 1 | 2 | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | – | 3 | 2 | |
| | | | 1 | 2 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 2 | |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | – | 3 | 2 | |
| | | | 1 | 2 | 8 |
STEP 13: DIVIDE 128 : 16 = 8 with a remainder of 0
|
| | | 0 | 1 | 2 | 8 |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | – | 3 | 2 | |
| | | | 1 | 2 | 8 |
STEP 14: MULTIPLY 8 · 16 = 128
|
| | | 0 | 1 | 2 | 8 |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | – | 3 | 2 | |
| | | | 1 | 2 | 8 |
| | | | 1 | 2 | 8 |
STEP 15: SUBTRACT 128 - 128 = 0
|
| | | 0 | 1 | 2 | 8 |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | – | 3 | 2 | |
| | | | 1 | 2 | 8 |
| | | – | 1 | 2 | 8 |
| | | | | | 0 |
STEP 15: SUBTRACT 128 - 128 = 0
|
| | | 0 | 1 | 2 | 8 |
| 1 | 6 | 2 | 0 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 0 | | |
| | – | 1 | 6 | | |
| | | | 4 | 4 | |
| | | – | 3 | 2 | |
| | | | 1 | 2 | 8 |
| | | – | 1 | 2 | 8 |
| | | | | | 0 |
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