Question
What is the quotient and remainder when $ 10123 $ is divided by $ 32 $ ?
Answer
The quotient is 316 and the remainder is 11.
Explanation
| Division Table | ||||||
| 0 | 0 | 3 | 1 | 6 | ||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| – | 3 | 2 | ||||
| 2 | 0 | 3 | ||||
| – | 1 | 9 | 2 | |||
| 1 | 1 | |||||
|
STEP 0: set up a division table |
||||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
|
STEP 1: DIVIDE 1 : 32 = 0 with a remainder of 1 |
||||||
| 0 | ||||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
|
STEP 2: MULTIPLY 0 · 32 = 0 |
||||||
| 0 | ||||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| 0 | ||||||
|
STEP 3: SUBTRACT 1 - 0 = 1 |
||||||
| 0 | ||||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | ||||||
| STEP 4: BRING DOWN | ||||||
| 0 | ||||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
|
STEP 5: DIVIDE 10 : 32 = 0 with a remainder of 10 |
||||||
| 0 | 0 | |||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
|
STEP 6: MULTIPLY 0 · 32 = 0 |
||||||
| 0 | 0 | |||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| 0 | ||||||
|
STEP 7: SUBTRACT 10 - 0 = 10 |
||||||
| 0 | 0 | |||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | |||||
| STEP 8: BRING DOWN | ||||||
| 0 | 0 | |||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
|
STEP 9: DIVIDE 101 : 32 = 3 with a remainder of 5 |
||||||
| 0 | 0 | 3 | ||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
|
STEP 10: MULTIPLY 3 · 32 = 96 |
||||||
| 0 | 0 | 3 | ||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| 9 | 6 | |||||
|
STEP 11: SUBTRACT 101 - 96 = 5 |
||||||
| 0 | 0 | 3 | ||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | ||||||
| STEP 12: BRING DOWN | ||||||
| 0 | 0 | 3 | ||||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
|
STEP 13: DIVIDE 52 : 32 = 1 with a remainder of 20 |
||||||
| 0 | 0 | 3 | 1 | |||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
|
STEP 14: MULTIPLY 1 · 32 = 32 |
||||||
| 0 | 0 | 3 | 1 | |||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| 3 | 2 | |||||
|
STEP 15: SUBTRACT 52 - 32 = 20 |
||||||
| 0 | 0 | 3 | 1 | |||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| – | 3 | 2 | ||||
| 2 | 0 | |||||
| STEP 16: BRING DOWN | ||||||
| 0 | 0 | 3 | 1 | |||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| – | 3 | 2 | ||||
| 2 | 0 | 3 | ||||
|
STEP 17: DIVIDE 203 : 32 = 6 with a remainder of 11 |
||||||
| 0 | 0 | 3 | 1 | 6 | ||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| – | 3 | 2 | ||||
| 2 | 0 | 3 | ||||
|
STEP 18: MULTIPLY 6 · 32 = 192 |
||||||
| 0 | 0 | 3 | 1 | 6 | ||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| – | 3 | 2 | ||||
| 2 | 0 | 3 | ||||
| 1 | 9 | 2 | ||||
|
STEP 19: SUBTRACT 203 - 192 = 11 |
||||||
| 0 | 0 | 3 | 1 | 6 | ||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| – | 3 | 2 | ||||
| 2 | 0 | 3 | ||||
| – | 1 | 9 | 2 | |||
| 1 | 1 | |||||
|
STEP 19: SUBTRACT 203 - 192 = 11 |
||||||
| 0 | 0 | 3 | 1 | 6 | ||
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| – | 0 | |||||
| 1 | 0 | |||||
| – | 0 | |||||
| 1 | 0 | 1 | ||||
| – | 9 | 6 | ||||
| 5 | 2 | |||||
| – | 3 | 2 | ||||
| 2 | 0 | 3 | ||||
| – | 1 | 9 | 2 | |||
| 1 | 1 | |||||
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