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Question
What is the quotient and remainder when $ 6572 $ is divided by $ 53 $ ?
Answer
The quotient is 124 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 1 | 2 | 4 |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | – | 1 | 0 | 6 | |
| | | | 2 | 1 | 2 |
| | | – | 2 | 1 | 2 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
STEP 1: DIVIDE 6 : 53 = 0 with a remainder of 6
|
| | | 0 | | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
STEP 2: MULTIPLY 0 · 53 = 0
|
| | | 0 | | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | | 0 | | | |
STEP 3: SUBTRACT 6 - 0 = 6
|
| | | 0 | | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
STEP 5: DIVIDE 65 : 53 = 1 with a remainder of 12
|
| | | 0 | 1 | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
STEP 6: MULTIPLY 1 · 53 = 53
|
| | | 0 | 1 | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | | 5 | 3 | | |
STEP 7: SUBTRACT 65 - 53 = 12
|
| | | 0 | 1 | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
STEP 9: DIVIDE 127 : 53 = 2 with a remainder of 21
|
| | | 0 | 1 | 2 | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
STEP 10: MULTIPLY 2 · 53 = 106
|
| | | 0 | 1 | 2 | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | | 1 | 0 | 6 | |
STEP 11: SUBTRACT 127 - 106 = 21
|
| | | 0 | 1 | 2 | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | – | 1 | 0 | 6 | |
| | | | 2 | 1 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 2 | |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | – | 1 | 0 | 6 | |
| | | | 2 | 1 | 2 |
STEP 13: DIVIDE 212 : 53 = 4 with a remainder of 0
|
| | | 0 | 1 | 2 | 4 |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | – | 1 | 0 | 6 | |
| | | | 2 | 1 | 2 |
STEP 14: MULTIPLY 4 · 53 = 212
|
| | | 0 | 1 | 2 | 4 |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | – | 1 | 0 | 6 | |
| | | | 2 | 1 | 2 |
| | | | 2 | 1 | 2 |
STEP 15: SUBTRACT 212 - 212 = 0
|
| | | 0 | 1 | 2 | 4 |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | – | 1 | 0 | 6 | |
| | | | 2 | 1 | 2 |
| | | – | 2 | 1 | 2 |
| | | | | | 0 |
STEP 15: SUBTRACT 212 - 212 = 0
|
| | | 0 | 1 | 2 | 4 |
| 5 | 3 | 6 | 5 | 7 | 2 |
| | – | 0 | | | |
| | | 6 | 5 | | |
| | – | 5 | 3 | | |
| | | 1 | 2 | 7 | |
| | – | 1 | 0 | 6 | |
| | | | 2 | 1 | 2 |
| | | – | 2 | 1 | 2 |
| | | | | | 0 |
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