SOLUTION: If p is the greatest prime factor of 34 and q is the greatest prime factor of 90, what is the greatest prime factor of the product pq ?

Here's a list of the first dozen prime numbers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

The largest number in that list of prime numbers 
that will divide evenly into 34 is 17.

So p is 17.

The largest number in that list that will divide 
evenly into 90 is 5.

So q is 5.

Since pq is 17x5 or 85, and there are only two prime factors of it,
17 and 5, obviously the larger one is 17.

Edwin