Question
What is the quotient and remainder when $ 5356 $ is divided by $ 213 $ ?
Answer
The quotient is 25 and the remainder is 31.
Explanation
| Division Table | ||||||
| 0 | 0 | 2 | 5 | |||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| – | 4 | 2 | 6 | |||
| 1 | 0 | 9 | 6 | |||
| – | 1 | 0 | 6 | 5 | ||
| 3 | 1 | |||||
|
STEP 0: set up a division table |
||||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
|
STEP 1: DIVIDE 5 : 213 = 0 with a remainder of 5 |
||||||
| 0 | ||||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
|
STEP 2: MULTIPLY 0 · 213 = 0 |
||||||
| 0 | ||||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| 0 | ||||||
|
STEP 3: SUBTRACT 5 - 0 = 5 |
||||||
| 0 | ||||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | ||||||
| STEP 4: BRING DOWN | ||||||
| 0 | ||||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
|
STEP 5: DIVIDE 53 : 213 = 0 with a remainder of 53 |
||||||
| 0 | 0 | |||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
|
STEP 6: MULTIPLY 0 · 213 = 0 |
||||||
| 0 | 0 | |||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| 0 | ||||||
|
STEP 7: SUBTRACT 53 - 0 = 53 |
||||||
| 0 | 0 | |||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | |||||
| STEP 8: BRING DOWN | ||||||
| 0 | 0 | |||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
|
STEP 9: DIVIDE 535 : 213 = 2 with a remainder of 109 |
||||||
| 0 | 0 | 2 | ||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
|
STEP 10: MULTIPLY 2 · 213 = 426 |
||||||
| 0 | 0 | 2 | ||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| 4 | 2 | 6 | ||||
|
STEP 11: SUBTRACT 535 - 426 = 109 |
||||||
| 0 | 0 | 2 | ||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| – | 4 | 2 | 6 | |||
| 1 | 0 | 9 | ||||
| STEP 12: BRING DOWN | ||||||
| 0 | 0 | 2 | ||||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| – | 4 | 2 | 6 | |||
| 1 | 0 | 9 | 6 | |||
|
STEP 13: DIVIDE 1096 : 213 = 5 with a remainder of 31 |
||||||
| 0 | 0 | 2 | 5 | |||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| – | 4 | 2 | 6 | |||
| 1 | 0 | 9 | 6 | |||
|
STEP 14: MULTIPLY 5 · 213 = 1065 |
||||||
| 0 | 0 | 2 | 5 | |||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| – | 4 | 2 | 6 | |||
| 1 | 0 | 9 | 6 | |||
| 1 | 0 | 6 | 5 | |||
|
STEP 15: SUBTRACT 1096 - 1065 = 31 |
||||||
| 0 | 0 | 2 | 5 | |||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| – | 4 | 2 | 6 | |||
| 1 | 0 | 9 | 6 | |||
| – | 1 | 0 | 6 | 5 | ||
| 3 | 1 | |||||
|
STEP 15: SUBTRACT 1096 - 1065 = 31 |
||||||
| 0 | 0 | 2 | 5 | |||
| 2 | 1 | 3 | 5 | 3 | 5 | 6 |
| – | 0 | |||||
| 5 | 3 | |||||
| – | 0 | |||||
| 5 | 3 | 5 | ||||
| – | 4 | 2 | 6 | |||
| 1 | 0 | 9 | 6 | |||
| – | 1 | 0 | 6 | 5 | ||
| 3 | 1 | |||||
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