Question
What is the quotient and remainder when $ 3756 $ is divided by $ 106 $ ?
Answer
The quotient is 35 and the remainder is 46.
Explanation
| Division Table | ||||||
| 0 | 0 | 3 | 5 | |||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| – | 3 | 1 | 8 | |||
| 5 | 7 | 6 | ||||
| – | 5 | 3 | 0 | |||
| 4 | 6 | |||||
|
STEP 0: set up a division table |
||||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
|
STEP 1: DIVIDE 3 : 106 = 0 with a remainder of 3 |
||||||
| 0 | ||||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
|
STEP 2: MULTIPLY 0 · 106 = 0 |
||||||
| 0 | ||||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| 0 | ||||||
|
STEP 3: SUBTRACT 3 - 0 = 3 |
||||||
| 0 | ||||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | ||||||
| STEP 4: BRING DOWN | ||||||
| 0 | ||||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
|
STEP 5: DIVIDE 37 : 106 = 0 with a remainder of 37 |
||||||
| 0 | 0 | |||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
|
STEP 6: MULTIPLY 0 · 106 = 0 |
||||||
| 0 | 0 | |||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| 0 | ||||||
|
STEP 7: SUBTRACT 37 - 0 = 37 |
||||||
| 0 | 0 | |||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | |||||
| STEP 8: BRING DOWN | ||||||
| 0 | 0 | |||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
|
STEP 9: DIVIDE 375 : 106 = 3 with a remainder of 57 |
||||||
| 0 | 0 | 3 | ||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
|
STEP 10: MULTIPLY 3 · 106 = 318 |
||||||
| 0 | 0 | 3 | ||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| 3 | 1 | 8 | ||||
|
STEP 11: SUBTRACT 375 - 318 = 57 |
||||||
| 0 | 0 | 3 | ||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| – | 3 | 1 | 8 | |||
| 5 | 7 | |||||
| STEP 12: BRING DOWN | ||||||
| 0 | 0 | 3 | ||||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| – | 3 | 1 | 8 | |||
| 5 | 7 | 6 | ||||
|
STEP 13: DIVIDE 576 : 106 = 5 with a remainder of 46 |
||||||
| 0 | 0 | 3 | 5 | |||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| – | 3 | 1 | 8 | |||
| 5 | 7 | 6 | ||||
|
STEP 14: MULTIPLY 5 · 106 = 530 |
||||||
| 0 | 0 | 3 | 5 | |||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| – | 3 | 1 | 8 | |||
| 5 | 7 | 6 | ||||
| 5 | 3 | 0 | ||||
|
STEP 15: SUBTRACT 576 - 530 = 46 |
||||||
| 0 | 0 | 3 | 5 | |||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| – | 3 | 1 | 8 | |||
| 5 | 7 | 6 | ||||
| – | 5 | 3 | 0 | |||
| 4 | 6 | |||||
|
STEP 15: SUBTRACT 576 - 530 = 46 |
||||||
| 0 | 0 | 3 | 5 | |||
| 1 | 0 | 6 | 3 | 7 | 5 | 6 |
| – | 0 | |||||
| 3 | 7 | |||||
| – | 0 | |||||
| 3 | 7 | 5 | ||||
| – | 3 | 1 | 8 | |||
| 5 | 7 | 6 | ||||
| – | 5 | 3 | 0 | |||
| 4 | 6 | |||||
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