Question 199000
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 ?

<pre><font size = 4 color = "indigo"><b>

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

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

</pre></b></font>
>>...p is the greatest prime factor of 34...<<
<pre><font size = 4 color = "indigo"><b>
The largest number in that list of prime numbers 
that will divide evenly into 34 is 17.

So p is 17.
</pre></b></font>
>>...q is the greatest prime factor of 90...<<
<pre><font size = 4 color = "indigo"><b>
The largest number in that list that will divide 
evenly into 90 is 5.

So q is 5.
</pre></b></font>
>>...what is the greatest prime factor of the product pq?...<<
<pre><font size = 4 color = "indigo"><b>
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</pre>