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Question
What is the quotient and remainder when $ 2248 $ is divided by $ 53 $ ?
Answer
The quotient is 42 and the remainder is 22.
Explanation
|
Division Table
|
| | | 0 | 0 | 4 | 2 |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | – | 2 | 1 | 2 | |
| | | | 1 | 2 | 8 |
| | | – | 1 | 0 | 6 |
| | | | | 2 | 2 |
STEP 0: set up a division table
|
| | | | | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
STEP 1: DIVIDE 2 : 53 = 0 with a remainder of 2
|
| | | 0 | | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
STEP 2: MULTIPLY 0 · 53 = 0
|
| | | 0 | | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
STEP 5: DIVIDE 22 : 53 = 0 with a remainder of 22
|
| | | 0 | 0 | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
STEP 6: MULTIPLY 0 · 53 = 0
|
| | | 0 | 0 | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 22 - 0 = 22
|
| | | 0 | 0 | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
STEP 9: DIVIDE 224 : 53 = 4 with a remainder of 12
|
| | | 0 | 0 | 4 | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
STEP 10: MULTIPLY 4 · 53 = 212
|
| | | 0 | 0 | 4 | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | | 2 | 1 | 2 | |
STEP 11: SUBTRACT 224 - 212 = 12
|
| | | 0 | 0 | 4 | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | – | 2 | 1 | 2 | |
| | | | 1 | 2 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 0 | 4 | |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | – | 2 | 1 | 2 | |
| | | | 1 | 2 | 8 |
STEP 13: DIVIDE 128 : 53 = 2 with a remainder of 22
|
| | | 0 | 0 | 4 | 2 |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | – | 2 | 1 | 2 | |
| | | | 1 | 2 | 8 |
STEP 14: MULTIPLY 2 · 53 = 106
|
| | | 0 | 0 | 4 | 2 |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | – | 2 | 1 | 2 | |
| | | | 1 | 2 | 8 |
| | | | 1 | 0 | 6 |
STEP 15: SUBTRACT 128 - 106 = 22
|
| | | 0 | 0 | 4 | 2 |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | – | 2 | 1 | 2 | |
| | | | 1 | 2 | 8 |
| | | – | 1 | 0 | 6 |
| | | | | 2 | 2 |
STEP 15: SUBTRACT 128 - 106 = 22
|
| | | 0 | 0 | 4 | 2 |
| 5 | 3 | 2 | 2 | 4 | 8 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 4 | |
| | – | 2 | 1 | 2 | |
| | | | 1 | 2 | 8 |
| | | – | 1 | 0 | 6 |
| | | | | 2 | 2 |
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