Find the largest possible number that may divide each of two numbers whose sum is $1394$, given that neither component number is zero or equal to each other.

Let the two numbers be $x$ and $y$, and let their highest common factor (HCF) be $g$.
Therefore, we can write $x=g\cdot a$ and $y=g\cdot b$, where $a$ and $b$ are co-prime positive integers ($\gcd (a,b)=1$).

Given:

$$x+y=1394⟹g(a+b)=1394$$

This means $g$ must be a factor of $1394$. Let's perform prime factorization on $1394$:

$$1394=2\times 697=2\times 17\times 41$$

The options available are $17,34,41,$ and $82$. To maximize the common factor $g$, let's check the largest option, $82$:
If $g=82$:

$$a+b=\frac{1394}{82}=17$$

Since the numbers cannot be equal, $a\ne b$. We can choose $a=1$ and $b=16$ (which are co-prime).
This gives valid distinct non-zero component numbers:

$$x=82\times 1=82$$

$$y=82\times 16=1312$$

Sum = $82+1312=1394$.

Hence, the largest possible number from the options is $82$.