Minimum number of components in graph
Yes, this is correct.

The easiest way to get to the result is to look at a graph with $v$ vertices and $0$ edges. It obviously has $v$ components. Adding an edge between two vertices $a$ and $b$ reduces the number of components if $a$ was not reachable from $b$ before adding the new edge.

Concerning  "best" solution: Your approach yields an optimal solution, though it is only one way to do it - there are other ways (e.g. 26 components with either 2 or 3 vertices) that work equally well.