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What is the quotient and remainder when $ 11208 $ is divided by $ 53 $ ?
Answer
The quotient is 211 and the remainder is 25.
Explanation
Division Table
|
| | 0 | 0 | 2 | 1 | 1 |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | – | 5 | 3 | |
| | | | | 7 | 8 |
| | | | – | 5 | 3 |
| | | | | 2 | 5 |
STEP 0: set up a division table
|
| | | | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
STEP 1: DIVIDE 1 : 53 = 0 with a remainder of 1
|
| | 0 | | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
STEP 2: MULTIPLY 0 · 53 = 0
|
| | 0 | | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| | 0 | | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | 0 | | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | | | | |
STEP 4: BRING DOWN
|
| | 0 | | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
STEP 5: DIVIDE 11 : 53 = 0 with a remainder of 11
|
| | 0 | 0 | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
STEP 6: MULTIPLY 0 · 53 = 0
|
| | 0 | 0 | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | | 0 | | | |
STEP 7: SUBTRACT 11 - 0 = 11
|
| | 0 | 0 | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | | | |
STEP 8: BRING DOWN
|
| | 0 | 0 | | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
STEP 9: DIVIDE 112 : 53 = 2 with a remainder of 6
|
| | 0 | 0 | 2 | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
STEP 10: MULTIPLY 2 · 53 = 106
|
| | 0 | 0 | 2 | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| | 1 | 0 | 6 | | |
STEP 11: SUBTRACT 112 - 106 = 6
|
| | 0 | 0 | 2 | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | | |
STEP 12: BRING DOWN
|
| | 0 | 0 | 2 | | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
STEP 13: DIVIDE 60 : 53 = 1 with a remainder of 7
|
| | 0 | 0 | 2 | 1 | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
STEP 14: MULTIPLY 1 · 53 = 53
|
| | 0 | 0 | 2 | 1 | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | | 5 | 3 | |
STEP 15: SUBTRACT 60 - 53 = 7
|
| | 0 | 0 | 2 | 1 | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | – | 5 | 3 | |
| | | | | 7 | |
STEP 16: BRING DOWN
|
| | 0 | 0 | 2 | 1 | |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | – | 5 | 3 | |
| | | | | 7 | 8 |
STEP 17: DIVIDE 78 : 53 = 1 with a remainder of 25
|
| | 0 | 0 | 2 | 1 | 1 |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | – | 5 | 3 | |
| | | | | 7 | 8 |
STEP 18: MULTIPLY 1 · 53 = 53
|
| | 0 | 0 | 2 | 1 | 1 |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | – | 5 | 3 | |
| | | | | 7 | 8 |
| | | | | 5 | 3 |
STEP 19: SUBTRACT 78 - 53 = 25
|
| | 0 | 0 | 2 | 1 | 1 |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | – | 5 | 3 | |
| | | | | 7 | 8 |
| | | | – | 5 | 3 |
| | | | | 2 | 5 |
STEP 19: SUBTRACT 78 - 53 = 25
|
| | 0 | 0 | 2 | 1 | 1 |
5 | 3 | 1 | 1 | 2 | 0 | 8 |
| – | 0 | | | | |
| | 1 | 1 | | | |
| | – | 0 | | | |
| | 1 | 1 | 2 | | |
| – | 1 | 0 | 6 | | |
| | | | 6 | 0 | |
| | | – | 5 | 3 | |
| | | | | 7 | 8 |
| | | | – | 5 | 3 |
| | | | | 2 | 5 |
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