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Question
What is the quotient and remainder when $ 3444 $ is divided by $ 21 $ ?
Answer
The quotient is 164 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 1 | 6 | 4 |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | – | 1 | 2 | 6 | |
| | | | | 8 | 4 |
| | | | – | 8 | 4 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
STEP 1: DIVIDE 3 : 21 = 0 with a remainder of 3
|
| | | 0 | | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
STEP 2: MULTIPLY 0 · 21 = 0
|
| | | 0 | | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
STEP 5: DIVIDE 34 : 21 = 1 with a remainder of 13
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
STEP 6: MULTIPLY 1 · 21 = 21
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | | 2 | 1 | | |
STEP 7: SUBTRACT 34 - 21 = 13
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
STEP 9: DIVIDE 134 : 21 = 6 with a remainder of 8
|
| | | 0 | 1 | 6 | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
STEP 10: MULTIPLY 6 · 21 = 126
|
| | | 0 | 1 | 6 | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | | 1 | 2 | 6 | |
STEP 11: SUBTRACT 134 - 126 = 8
|
| | | 0 | 1 | 6 | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | – | 1 | 2 | 6 | |
| | | | | 8 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 6 | |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | – | 1 | 2 | 6 | |
| | | | | 8 | 4 |
STEP 13: DIVIDE 84 : 21 = 4 with a remainder of 0
|
| | | 0 | 1 | 6 | 4 |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | – | 1 | 2 | 6 | |
| | | | | 8 | 4 |
STEP 14: MULTIPLY 4 · 21 = 84
|
| | | 0 | 1 | 6 | 4 |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | – | 1 | 2 | 6 | |
| | | | | 8 | 4 |
| | | | | 8 | 4 |
STEP 15: SUBTRACT 84 - 84 = 0
|
| | | 0 | 1 | 6 | 4 |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | – | 1 | 2 | 6 | |
| | | | | 8 | 4 |
| | | | – | 8 | 4 |
| | | | | | 0 |
STEP 15: SUBTRACT 84 - 84 = 0
|
| | | 0 | 1 | 6 | 4 |
| 2 | 1 | 3 | 4 | 4 | 4 |
| | – | 0 | | | |
| | | 3 | 4 | | |
| | – | 2 | 1 | | |
| | | 1 | 3 | 4 | |
| | – | 1 | 2 | 6 | |
| | | | | 8 | 4 |
| | | | – | 8 | 4 |
| | | | | | 0 |
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