$3$ children riddle, compute the ages based on information given A man has $3$ children such that their ages add up to some number $x$, and whose ages multiply to some number $y$, such that $xy = 756$.  What are the ages of the $3$ children?
Letting the ages be $a$, $b$, and $c$ of the three children, what we know is the following.
$$a+b+c = x$$
$$abc = y$$
$$xy = 756.$$
How can I go about solving this?  I tried just plugging in some numbers and can get semi close such as ages $3,3,7$ which gives an $xy$ value of $819$.
Also I tried working backwards from $756$ to divide thru  by factors and I got $378,189,63,21,7$, which is why I thought one of the ages might be $7$.

There is also another "reasonable" solution which is the ages are $3.5$, $4$, and $4.5$.  Some children's ages are expressed in "halves" although it is not as common as "wholes".  ($3.5 + 4 + 4.5$) * ($3.5 * 4 * 4.5$) does indeed equal $756$.  It is interesting to note that this is $12 * 63$ and if you were to guess the ages were $4,4,4$, that would give you $12 * 64$ which is very close to the correct answer of $12 * 63$ so that would imply that the ages have to all be very close to $4$ meaning they are likely not all integers.  Ages $3,4,5$ is also a near solution at $12*60=720$.
