Why is Binary Search a divide and conquer algorithm?

Question

I was asked if a Binary Search is a divide and conquer algorithm at an exam. My answer was yes, because you divided the problem into smaller subproblems, until you reached y

Answer 1

The Binary Search is a divide and conquer algorithm:

1) In Divide and Conquer algorithms, we try to solve a problem by solving a smaller sub problem (Divide part) and use the solution to build the solution for our bigger problem(Conquer).

2) Here our problem is to find an element in the sorted array. We can solve this by solving a similar sub problem. (We are creating sub problems here based on a decision that the element being searched is smaller or bigger than the middle element). Thus once we know that the element can not exist surely in one half, we solve a similar sub-problem in the the other half.

3) This way we recurse.

4) The conquer part here is just returning the value returned by the sub problem to the top the recursive tree