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Question
What is the quotient and remainder when $ 3028 $ is divided by $ 16 $ ?
Answer
The quotient is 189 and the remainder is 4.
Explanation
|
Division Table
|
| | | 0 | 1 | 8 | 9 |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | – | 1 | 2 | 8 | |
| | | | 1 | 4 | 8 |
| | | – | 1 | 4 | 4 |
| | | | | | 4 |
STEP 0: set up a division table
|
| | | | | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
STEP 1: DIVIDE 3 : 16 = 0 with a remainder of 3
|
| | | 0 | | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
STEP 2: MULTIPLY 0 · 16 = 0
|
| | | 0 | | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
STEP 5: DIVIDE 30 : 16 = 1 with a remainder of 14
|
| | | 0 | 1 | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
STEP 6: MULTIPLY 1 · 16 = 16
|
| | | 0 | 1 | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | | 1 | 6 | | |
STEP 7: SUBTRACT 30 - 16 = 14
|
| | | 0 | 1 | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
STEP 9: DIVIDE 142 : 16 = 8 with a remainder of 14
|
| | | 0 | 1 | 8 | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
STEP 10: MULTIPLY 8 · 16 = 128
|
| | | 0 | 1 | 8 | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | | 1 | 2 | 8 | |
STEP 11: SUBTRACT 142 - 128 = 14
|
| | | 0 | 1 | 8 | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | – | 1 | 2 | 8 | |
| | | | 1 | 4 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 8 | |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | – | 1 | 2 | 8 | |
| | | | 1 | 4 | 8 |
STEP 13: DIVIDE 148 : 16 = 9 with a remainder of 4
|
| | | 0 | 1 | 8 | 9 |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | – | 1 | 2 | 8 | |
| | | | 1 | 4 | 8 |
STEP 14: MULTIPLY 9 · 16 = 144
|
| | | 0 | 1 | 8 | 9 |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | – | 1 | 2 | 8 | |
| | | | 1 | 4 | 8 |
| | | | 1 | 4 | 4 |
STEP 15: SUBTRACT 148 - 144 = 4
|
| | | 0 | 1 | 8 | 9 |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | – | 1 | 2 | 8 | |
| | | | 1 | 4 | 8 |
| | | – | 1 | 4 | 4 |
| | | | | | 4 |
STEP 15: SUBTRACT 148 - 144 = 4
|
| | | 0 | 1 | 8 | 9 |
| 1 | 6 | 3 | 0 | 2 | 8 |
| | – | 0 | | | |
| | | 3 | 0 | | |
| | – | 1 | 6 | | |
| | | 1 | 4 | 2 | |
| | – | 1 | 2 | 8 | |
| | | | 1 | 4 | 8 |
| | | – | 1 | 4 | 4 |
| | | | | | 4 |
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