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Question
What is the quotient and remainder when $ 2593 $ is divided by $ 21 $ ?
Answer
The quotient is 123 and the remainder is 10.
Explanation
|
Division Table
|
| | | 0 | 1 | 2 | 3 |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | – | 4 | 2 | |
| | | | | 7 | 3 |
| | | | – | 6 | 3 |
| | | | | 1 | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
STEP 1: DIVIDE 2 : 21 = 0 with a remainder of 2
|
| | | 0 | | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
STEP 2: MULTIPLY 0 · 21 = 0
|
| | | 0 | | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
STEP 5: DIVIDE 25 : 21 = 1 with a remainder of 4
|
| | | 0 | 1 | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
STEP 6: MULTIPLY 1 · 21 = 21
|
| | | 0 | 1 | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | | 2 | 1 | | |
STEP 7: SUBTRACT 25 - 21 = 4
|
| | | 0 | 1 | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
STEP 9: DIVIDE 49 : 21 = 2 with a remainder of 7
|
| | | 0 | 1 | 2 | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
STEP 10: MULTIPLY 2 · 21 = 42
|
| | | 0 | 1 | 2 | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | | 4 | 2 | |
STEP 11: SUBTRACT 49 - 42 = 7
|
| | | 0 | 1 | 2 | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | – | 4 | 2 | |
| | | | | 7 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 2 | |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | – | 4 | 2 | |
| | | | | 7 | 3 |
STEP 13: DIVIDE 73 : 21 = 3 with a remainder of 10
|
| | | 0 | 1 | 2 | 3 |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | – | 4 | 2 | |
| | | | | 7 | 3 |
STEP 14: MULTIPLY 3 · 21 = 63
|
| | | 0 | 1 | 2 | 3 |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | – | 4 | 2 | |
| | | | | 7 | 3 |
| | | | | 6 | 3 |
STEP 15: SUBTRACT 73 - 63 = 10
|
| | | 0 | 1 | 2 | 3 |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | – | 4 | 2 | |
| | | | | 7 | 3 |
| | | | – | 6 | 3 |
| | | | | 1 | 0 |
STEP 15: SUBTRACT 73 - 63 = 10
|
| | | 0 | 1 | 2 | 3 |
| 2 | 1 | 2 | 5 | 9 | 3 |
| | – | 0 | | | |
| | | 2 | 5 | | |
| | – | 2 | 1 | | |
| | | | 4 | 9 | |
| | | – | 4 | 2 | |
| | | | | 7 | 3 |
| | | | – | 6 | 3 |
| | | | | 1 | 0 |
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