SOLUTION: You were assigned a locker for your books at school. You forgot the locker number but remmeber that two of the 12 positive factors of the locker number are 6 and 25. What is your l

Question 565018: You were assigned a locker for your books at school. You forgot the locker number but remmeber that two of the 12 positive factors of the locker number are 6 and 25. What is your locker number? Show or explain how you got your answer.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If two of the positive factors of the number are
and ,
the number must be a multiple of
The number 150 has positive factors.
Any other number who has 6 and 25 as factors will be a multiple of 150, and will have more than 12 factors.
So your locker is number 150.
How do I know has positive factors?
Because all the factors will be of the form
where a and b could be 0 or 1, and c could be 0, 1, or 2.
That gives you 2 choices for a, 2 choices for b,and 3 choices for c. That makes combinations.
In case you don't believe, I'll list the factors of 150

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