Question 1186009
.
The product of the ages, in years, of three teenagers is 4590. None of the teens are the same age. 
What are the ages of the teenagers?
~~~~~~~~~~~~~~


<pre>
They want you present the number 4590 as the product of three positive integer different numbers 
from the interval 13 to 19 inclusive.


Start finding prime divisors of the number 4590.

It is not so difficult as it may seem at the beginning.



First, there is a factor 10, which is the product of 2 and 5.


Divided by 10, the number 4590 gives the quotient 459.



The number 459 has the sum of the digits  4+5+9 = 18,  which is divisible by 9.

So, according to the divisibility by 9 rule, the number 459 is divisible by 9 = 3*3.

The quotient is 459/9 = 51.



Next, 51 = 17*3.


    +---------------------------------------------+        
    |    Thus 4590 = 10 * 9 * 17*3 = 2*5*3^3*17.  |
    +---------------------------------------------+        



17 is one of the targeted factors.


Next, it is obvious that the other targeted factor is 3*5 = 15.


The remaining factor is  {{{4590/(17*15)}}} = 18.


So, we just found the answer in this way: 4590 = 15*17*18.


<U>CHECK</U>.  15*17*18 = 4590.    ! Correct !
</pre>

Solved.



///////////



Instructions, &nbsp;attached at the end of your post, &nbsp;only &nbsp;INTERFERE &nbsp;with solving the problem.


The thoughts of a student, &nbsp;who solves a problem (any problem), &nbsp;should not be directed by any instructions:

they should flow / (fly) freely, &nbsp;without any restrictions.