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Question
What is the quotient and remainder when $ 26893 $ is divided by $ 21 $ ?
Answer
The quotient is 1280 and the remainder is 13.
Explanation
|
Division Table
|
| | | 0 | 1 | 2 | 8 | 0 |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | – | 1 | 6 | 8 | |
| | | | | | 1 | 3 |
| | | | | | – | 0 |
| | | | | | 1 | 3 |
STEP 0: set up a division table
|
| | | | | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
STEP 1: DIVIDE 2 : 21 = 0 with a remainder of 2
|
| | | 0 | | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
STEP 2: MULTIPLY 0 · 21 = 0
|
| | | 0 | | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | | 0 | | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
STEP 5: DIVIDE 26 : 21 = 1 with a remainder of 5
|
| | | 0 | 1 | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
STEP 6: MULTIPLY 1 · 21 = 21
|
| | | 0 | 1 | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | | 2 | 1 | | | |
STEP 7: SUBTRACT 26 - 21 = 5
|
| | | 0 | 1 | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
STEP 9: DIVIDE 58 : 21 = 2 with a remainder of 16
|
| | | 0 | 1 | 2 | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
STEP 10: MULTIPLY 2 · 21 = 42
|
| | | 0 | 1 | 2 | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | | 4 | 2 | | |
STEP 11: SUBTRACT 58 - 42 = 16
|
| | | 0 | 1 | 2 | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 2 | | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
STEP 13: DIVIDE 169 : 21 = 8 with a remainder of 1
|
| | | 0 | 1 | 2 | 8 | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
STEP 14: MULTIPLY 8 · 21 = 168
|
| | | 0 | 1 | 2 | 8 | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | | 1 | 6 | 8 | |
STEP 15: SUBTRACT 169 - 168 = 1
|
| | | 0 | 1 | 2 | 8 | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | – | 1 | 6 | 8 | |
| | | | | | 1 | |
|
STEP 16: BRING DOWN
|
| | | 0 | 1 | 2 | 8 | |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | – | 1 | 6 | 8 | |
| | | | | | 1 | 3 |
STEP 17: DIVIDE 13 : 21 = 0 with a remainder of 13
|
| | | 0 | 1 | 2 | 8 | 0 |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | – | 1 | 6 | 8 | |
| | | | | | 1 | 3 |
STEP 18: MULTIPLY 0 · 21 = 0
|
| | | 0 | 1 | 2 | 8 | 0 |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | – | 1 | 6 | 8 | |
| | | | | | 1 | 3 |
| | | | | | | 0 |
STEP 19: SUBTRACT 13 - 0 = 13
|
| | | 0 | 1 | 2 | 8 | 0 |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | – | 1 | 6 | 8 | |
| | | | | | 1 | 3 |
| | | | | | – | 0 |
| | | | | | 1 | 3 |
STEP 19: SUBTRACT 13 - 0 = 13
|
| | | 0 | 1 | 2 | 8 | 0 |
| 2 | 1 | 2 | 6 | 8 | 9 | 3 |
| | – | 0 | | | | |
| | | 2 | 6 | | | |
| | – | 2 | 1 | | | |
| | | | 5 | 8 | | |
| | | – | 4 | 2 | | |
| | | | 1 | 6 | 9 | |
| | | – | 1 | 6 | 8 | |
| | | | | | 1 | 3 |
| | | | | | – | 0 |
| | | | | | 1 | 3 |
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