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What is the quotient and remainder when $ 72456721 $ is divided by $ 18 $ ?
Answer
The quotient is 4025373 and the remainder is 7.
Explanation
Division Table
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | 3 |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | – | 1 | 2 | 6 | | |
| | | | | | | 6 | 1 | |
| | | | | | – | 5 | 4 | |
| | | | | | | | 7 | |
STEP 0: set up a division table
|
| | | | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
STEP 1: DIVIDE 7 : 18 = 0 with a remainder of 7
|
| | 0 | | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
STEP 2: MULTIPLY 0 · 18 = 0
|
| | 0 | | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| | 0 | | | | | | | |
STEP 3: SUBTRACT 7 - 0 = 7
|
| | 0 | | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | | | | | | | |
STEP 4: BRING DOWN
|
| | 0 | | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
STEP 5: DIVIDE 72 : 18 = 4 with a remainder of 0
|
| | 0 | 4 | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
STEP 6: MULTIPLY 4 · 18 = 72
|
| | 0 | 4 | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| | 7 | 2 | | | | | | |
STEP 7: SUBTRACT 72 - 72 = 0
|
| | 0 | 4 | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 0 | | | | | | |
STEP 8: BRING DOWN
|
| | 0 | 4 | | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
STEP 9: DIVIDE 4 : 18 = 0 with a remainder of 4
|
| | 0 | 4 | 0 | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
STEP 10: MULTIPLY 0 · 18 = 0
|
| | 0 | 4 | 0 | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | | 0 | | | | | | |
STEP 11: SUBTRACT 4 - 0 = 4
|
| | 0 | 4 | 0 | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | | | | | | |
STEP 12: BRING DOWN
|
| | 0 | 4 | 0 | | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
STEP 13: DIVIDE 45 : 18 = 2 with a remainder of 9
|
| | 0 | 4 | 0 | 2 | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
STEP 14: MULTIPLY 2 · 18 = 36
|
| | 0 | 4 | 0 | 2 | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | | 3 | 6 | | | | | |
STEP 15: SUBTRACT 45 - 36 = 9
|
| | 0 | 4 | 0 | 2 | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | | | | | |
STEP 16: BRING DOWN
|
| | 0 | 4 | 0 | 2 | | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
STEP 17: DIVIDE 96 : 18 = 5 with a remainder of 6
|
| | 0 | 4 | 0 | 2 | 5 | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
STEP 18: MULTIPLY 5 · 18 = 90
|
| | 0 | 4 | 0 | 2 | 5 | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | | 9 | 0 | | | | |
STEP 19: SUBTRACT 96 - 90 = 6
|
| | 0 | 4 | 0 | 2 | 5 | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | | | | |
STEP 20: BRING DOWN
|
| | 0 | 4 | 0 | 2 | 5 | | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
STEP 21: DIVIDE 67 : 18 = 3 with a remainder of 13
|
| | 0 | 4 | 0 | 2 | 5 | 3 | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
STEP 22: MULTIPLY 3 · 18 = 54
|
| | 0 | 4 | 0 | 2 | 5 | 3 | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | | 5 | 4 | | | |
STEP 23: SUBTRACT 67 - 54 = 13
|
| | 0 | 4 | 0 | 2 | 5 | 3 | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | | | |
STEP 24: BRING DOWN
|
| | 0 | 4 | 0 | 2 | 5 | 3 | | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
STEP 25: DIVIDE 132 : 18 = 7 with a remainder of 6
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
STEP 26: MULTIPLY 7 · 18 = 126
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | | 1 | 2 | 6 | | |
STEP 27: SUBTRACT 132 - 126 = 6
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | – | 1 | 2 | 6 | | |
| | | | | | | 6 | | |
STEP 28: BRING DOWN
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | – | 1 | 2 | 6 | | |
| | | | | | | 6 | 1 | |
STEP 29: DIVIDE 61 : 18 = 3 with a remainder of 7
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | 3 |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | – | 1 | 2 | 6 | | |
| | | | | | | 6 | 1 | |
STEP 30: MULTIPLY 3 · 18 = 54
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | 3 |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | – | 1 | 2 | 6 | | |
| | | | | | | 6 | 1 | |
| | | | | | | 5 | 4 | |
STEP 31: SUBTRACT 61 - 54 = 7
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | 3 |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | – | 1 | 2 | 6 | | |
| | | | | | | 6 | 1 | |
| | | | | | – | 5 | 4 | |
| | | | | | | | 7 | |
STEP 31: SUBTRACT 61 - 54 = 7
|
| | 0 | 4 | 0 | 2 | 5 | 3 | 7 | 3 |
1 | 8 | 7 | 2 | 4 | 5 | 6 | 7 | 2 | 1 |
| – | 0 | | | | | | | |
| | 7 | 2 | | | | | | |
| – | 7 | 2 | | | | | | |
| | | 4 | | | | | | |
| | – | 0 | | | | | | |
| | | 4 | 5 | | | | | |
| | – | 3 | 6 | | | | | |
| | | | 9 | 6 | | | | |
| | | – | 9 | 0 | | | | |
| | | | | 6 | 7 | | | |
| | | | – | 5 | 4 | | | |
| | | | | 1 | 3 | 2 | | |
| | | | – | 1 | 2 | 6 | | |
| | | | | | | 6 | 1 | |
| | | | | | – | 5 | 4 | |
| | | | | | | | 7 | |
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