Categorization of Binary search as Divide and Conquer
This might seem silly but here we go.

Let our array be $A$ and the current range we are searching in be denoted as $[L,R]$ and let $mid = \frac{L+R}{2}$. 


The divide step - We divide our search space into two ranges - $[L,mid-1]$ and $[mid,R]$.
The conquer step - Let's assume that WLOG the element $x$ that we are searching for is such that $x &lt; A[mid]$. Then we combine the knowledge that $x$ can be in $[L,mid)$ and $x$ cannot be in $[mid,R]$ to reduce our search space to $[L',R'] = [L,mid-1]$