Question
What is the quotient and remainder when $ 1345 $ is divided by $ 123 $ ?
Answer
The quotient is 10 and the remainder is 115.
Explanation
| Division Table | ||||||
| 0 | 0 | 1 | 0 | |||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| – | 1 | 2 | 3 | |||
| 1 | 1 | 5 | ||||
| – | 0 | |||||
| 1 | 1 | 5 | ||||
|
STEP 0: set up a division table |
||||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
|
STEP 1: DIVIDE 1 : 123 = 0 with a remainder of 1 |
||||||
| 0 | ||||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
|
STEP 2: MULTIPLY 0 · 123 = 0 |
||||||
| 0 | ||||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| 0 | ||||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
||||||
| 0 | ||||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | ||||||
| STEP 4: BRING DOWN | ||||||
| 0 | ||||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
|
STEP 5: DIVIDE 13 : 123 = 0 with a remainder of 13 |
||||||
| 0 | 0 | |||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
|
STEP 6: MULTIPLY 0 · 123 = 0 |
||||||
| 0 | 0 | |||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| 0 | ||||||
|
STEP 7: SUBTRACT 13 - 0 = 13 |
||||||
| 0 | 0 | |||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | |||||
| STEP 8: BRING DOWN | ||||||
| 0 | 0 | |||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
|
STEP 9: DIVIDE 134 : 123 = 1 with a remainder of 11 |
||||||
| 0 | 0 | 1 | ||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
|
STEP 10: MULTIPLY 1 · 123 = 123 |
||||||
| 0 | 0 | 1 | ||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| 1 | 2 | 3 | ||||
|
STEP 11: SUBTRACT 134 - 123 = 11 |
||||||
| 0 | 0 | 1 | ||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| – | 1 | 2 | 3 | |||
| 1 | 1 | |||||
| STEP 12: BRING DOWN | ||||||
| 0 | 0 | 1 | ||||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| – | 1 | 2 | 3 | |||
| 1 | 1 | 5 | ||||
|
STEP 13: DIVIDE 115 : 123 = 0 with a remainder of 115 |
||||||
| 0 | 0 | 1 | 0 | |||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| – | 1 | 2 | 3 | |||
| 1 | 1 | 5 | ||||
|
STEP 14: MULTIPLY 0 · 123 = 0 |
||||||
| 0 | 0 | 1 | 0 | |||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| – | 1 | 2 | 3 | |||
| 1 | 1 | 5 | ||||
| 0 | ||||||
|
STEP 15: SUBTRACT 115 - 0 = 115 |
||||||
| 0 | 0 | 1 | 0 | |||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| – | 1 | 2 | 3 | |||
| 1 | 1 | 5 | ||||
| – | 0 | |||||
| 1 | 1 | 5 | ||||
|
STEP 15: SUBTRACT 115 - 0 = 115 |
||||||
| 0 | 0 | 1 | 0 | |||
| 1 | 2 | 3 | 1 | 3 | 4 | 5 |
| – | 0 | |||||
| 1 | 3 | |||||
| – | 0 | |||||
| 1 | 3 | 4 | ||||
| – | 1 | 2 | 3 | |||
| 1 | 1 | 5 | ||||
| – | 0 | |||||
| 1 | 1 | 5 | ||||
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