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

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Question 565017: You were assigned a locker for your books at school. You forgot the locker number but remember 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 issacodegard(60) (Show Source):
You can put this solution on YOUR website!
We know that 6=2*3 and 25=5*5. Since 6 and 25 are divisors of the locker number call it x, and since 6 and 25 have no common prime factors, 2*3*5*5 must be a divisor of x. Therefore, 1, 2, 3, 5, 5*5, 2*3, 2*5, 2*5*5, 3*5, 3*5*5, 2*3*5, 2*3*5*5 are distinct divisors of x. But there are 12 divisors listed, so they must be the only 12 divisors of x. So the 2*3*5*5=150 must be the locker number.