Question 86
Using digits $a,b,c$, form the three-digit number $abc$ and the two-digit numbers $ab,bc,ca$. Find all values of $a,b,c$ such that
$$\frac{abc+a+b+c}{ab+bc+ca}$$
is an integer.
Hint: Show that the denominator is always divisible by $11$ and that $a+c=11$.
$$\frac{abc+a+b+c}{ab+bc+ca}$$
is an integer.
Hint: Show that the denominator is always divisible by $11$ and that $a+c=11$.