A knot is a closed curve in $\mathbb{R}^3$ which does not intersect itself. If two curves can be deformed continuously one into the other, these represent the same knot. One objective in Knot Theory is to distinguish them up to a continuous deformation. To do this, we use invariants, one of them being the number of r-colorings. A $r$-coloring is an assignment of integers in $\mathbb{Z}_r$ (colors) to the arcs of a knot diagram (projection of a knot in $\mathbb{R}^2$), such that, at each crossing twice the color of the over arc equals $(\mod r)$ the sum of the colors of the under arcs. Assigning the same color to each of the arcs always sets a trivial coloring. But, when do non-trivial colorings exist? And what will be the minimum number of colors used in a non-trivial coloring? To determine this invariant we would have to compute the minimum number of colors for all the (infinitely many) diagrams of a knot! However, it is possible to estimate this minimum for some classes of knots and, sometimes, calculate its exact value. In this talk we will present our results on minimum number of colors for the Turk's head knot.