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Question
What is the quotient and remainder when $ 3761 $ is divided by $ 21 $ ?
Answer
The quotient is 179 and the remainder is 2.
Explanation
|
Division Table
|
| | | 0 | 1 | 7 | 9 |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | – | 1 | 4 | 7 | |
| | | | 1 | 9 | 1 |
| | | – | 1 | 8 | 9 |
| | | | | | 2 |
STEP 0: set up a division table
|
| | | | | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
STEP 1: DIVIDE 3 : 21 = 0 with a remainder of 3
|
| | | 0 | | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
STEP 2: MULTIPLY 0 · 21 = 0
|
| | | 0 | | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
STEP 5: DIVIDE 37 : 21 = 1 with a remainder of 16
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
STEP 6: MULTIPLY 1 · 21 = 21
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | | 2 | 1 | | |
STEP 7: SUBTRACT 37 - 21 = 16
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
STEP 9: DIVIDE 166 : 21 = 7 with a remainder of 19
|
| | | 0 | 1 | 7 | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
STEP 10: MULTIPLY 7 · 21 = 147
|
| | | 0 | 1 | 7 | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | | 1 | 4 | 7 | |
STEP 11: SUBTRACT 166 - 147 = 19
|
| | | 0 | 1 | 7 | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | – | 1 | 4 | 7 | |
| | | | 1 | 9 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 7 | |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | – | 1 | 4 | 7 | |
| | | | 1 | 9 | 1 |
STEP 13: DIVIDE 191 : 21 = 9 with a remainder of 2
|
| | | 0 | 1 | 7 | 9 |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | – | 1 | 4 | 7 | |
| | | | 1 | 9 | 1 |
STEP 14: MULTIPLY 9 · 21 = 189
|
| | | 0 | 1 | 7 | 9 |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | – | 1 | 4 | 7 | |
| | | | 1 | 9 | 1 |
| | | | 1 | 8 | 9 |
STEP 15: SUBTRACT 191 - 189 = 2
|
| | | 0 | 1 | 7 | 9 |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | – | 1 | 4 | 7 | |
| | | | 1 | 9 | 1 |
| | | – | 1 | 8 | 9 |
| | | | | | 2 |
STEP 15: SUBTRACT 191 - 189 = 2
|
| | | 0 | 1 | 7 | 9 |
| 2 | 1 | 3 | 7 | 6 | 1 |
| | – | 0 | | | |
| | | 3 | 7 | | |
| | – | 2 | 1 | | |
| | | 1 | 6 | 6 | |
| | – | 1 | 4 | 7 | |
| | | | 1 | 9 | 1 |
| | | – | 1 | 8 | 9 |
| | | | | | 2 |
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