factors problem

[dibilo]

Find a whole number for which the sum of its two largest factors is 340.


pls offer help ... what method can i use to slove such a problem??

[TenaliRaman]

Let n be the number we want ...
Let x and y be its largest factors ....

we know,
xy=n ...
(pedantically xy = nk where k is some integer but it that would mean i can find a factor greater than x or y)

and x+y = 340

y=n/x
so x+n/x = 340

ok now try to proceed from here ...

-- AI

[HallsofIvy]

Note: there are, of course, an infinite number of correct solutions.