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What is the quotient and remainder when $ 10640 $ is divided by $ 103 $ ?
Answer
The quotient is 103 and the remainder is 31.
Explanation
|
Division Table
|
| | | | 0 | 0 | 1 | 0 | 3 |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | – | 0 | |
| | | | | | 3 | 4 | 0 |
| | | | | – | 3 | 0 | 9 |
| | | | | | | 3 | 1 |
STEP 0:
set up a division table
|
| | | | | | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
STEP 1: DIVIDE
1 : 103 = 0 with a remainder of 1
|
| | | | 0 | | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
STEP 2: MULTIPLY
0 · 103 = 0
|
| | | | 0 | | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | | 0 | | | | |
STEP 3: SUBTRACT
1 - 0 = 1
|
| | | | 0 | | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | | | | |
|
STEP 4: BRING DOWN
|
| | | | 0 | | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
STEP 5: DIVIDE
10 : 103 = 0 with a remainder of 10
|
| | | | 0 | 0 | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
STEP 6: MULTIPLY
0 · 103 = 0
|
| | | | 0 | 0 | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | | 0 | | | |
STEP 7: SUBTRACT
10 - 0 = 10
|
| | | | 0 | 0 | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | | | |
|
STEP 8: BRING DOWN
|
| | | | 0 | 0 | | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
STEP 9: DIVIDE
106 : 103 = 1 with a remainder of 3
|
| | | | 0 | 0 | 1 | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
STEP 10: MULTIPLY
1 · 103 = 103
|
| | | | 0 | 0 | 1 | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | | 1 | 0 | 3 | | |
STEP 11: SUBTRACT
106 - 103 = 3
|
| | | | 0 | 0 | 1 | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | | |
|
STEP 12: BRING DOWN
|
| | | | 0 | 0 | 1 | | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
STEP 13: DIVIDE
34 : 103 = 0 with a remainder of 34
|
| | | | 0 | 0 | 1 | 0 | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
STEP 14: MULTIPLY
0 · 103 = 0
|
| | | | 0 | 0 | 1 | 0 | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | | 0 | |
STEP 15: SUBTRACT
34 - 0 = 34
|
| | | | 0 | 0 | 1 | 0 | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | – | 0 | |
| | | | | | 3 | 4 | |
|
STEP 16: BRING DOWN
|
| | | | 0 | 0 | 1 | 0 | |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | – | 0 | |
| | | | | | 3 | 4 | 0 |
STEP 17: DIVIDE
340 : 103 = 3 with a remainder of 31
|
| | | | 0 | 0 | 1 | 0 | 3 |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | – | 0 | |
| | | | | | 3 | 4 | 0 |
STEP 18: MULTIPLY
3 · 103 = 309
|
| | | | 0 | 0 | 1 | 0 | 3 |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | – | 0 | |
| | | | | | 3 | 4 | 0 |
| | | | | | 3 | 0 | 9 |
STEP 19: SUBTRACT
340 - 309 = 31
|
| | | | 0 | 0 | 1 | 0 | 3 |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | – | 0 | |
| | | | | | 3 | 4 | 0 |
| | | | | – | 3 | 0 | 9 |
| | | | | | | 3 | 1 |
STEP 19: SUBTRACT
340 - 309 = 31
|
| | | | 0 | 0 | 1 | 0 | 3 |
| 1 | 0 | 3 | 1 | 0 | 6 | 4 | 0 |
| | | – | 0 | | | | |
| | | | 1 | 0 | | | |
| | | | – | 0 | | | |
| | | | 1 | 0 | 6 | | |
| | | – | 1 | 0 | 3 | | |
| | | | | | 3 | 4 | |
| | | | | | – | 0 | |
| | | | | | 3 | 4 | 0 |
| | | | | – | 3 | 0 | 9 |
| | | | | | | 3 | 1 |
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