|
Question 130404: A mystery number less then 20 has factors. Three of its factors are consecutive odd number. What is the number?
Found 2 solutions by solver91311, checkley71:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! In fact there are an infinite number of solutions to this problem because nowhere does it say that either the number itself or any of its factors must be positive. The product of ANY three consecutive negative odd integers is itself less than zero and therefore less than 20.
If you restrict the factors to the set of positive odd integers, then there is only one answer. The smallest positive odd integer is 1, the next consecutive odd integer is 3, and the third is 5. Their product is 15. The next smallest set of consecutive odd integers is 3, 5, and 7 whose product is 105 -- much too large.
Note that this is much more restrictive than the problem statement either says or implies. The language: "Three of the factors are..." certainly allows the possibility of more than three factors for the number with no restrictions whatsoever on the character of any factors in excess of three -- a possible 4th factor doesn't necessarily need to be an integer or even rational for that matter. So, again we could come up with an infinite set of solutions if you only allowed a 4th factor. Example: Let the 4th factor be  . That would make the mystery number just a tiny bit larger than 15. But there are an infinite number of possible 4th factors that allow for a result less than 20.
You must also restrict the number itself to the positive integers, because if there were a 4th factor, we could say the 4 factors are 77, 79, 81, and -1, and the product is -492723 which is very much smaller than 20.
So, given that you restrict the factors to the set of positive integers, the number itself to the positive integers, and the number of factors to exactly 3, the mystery number is 15. Without such restrictions, the mystery number will remain a mystery.
Answer by checkley71(8403)  (Show Source):
|
|
|
| |
