Orange crystals used in the laboratory are 26.6% potassium, 35.4% chromium and 38.0% oxygen by mass…

Step 1. Moles in 100 g. Potassium: $\dfrac{26.6}{39} = 0.682\ \text{mol}$. Chromium: $\dfrac{35.4}{52} = 0.681\ \text{mol}$. Oxygen: $\dfrac{38.0}{16} = 2.375\ \text{mol}$.

Step 2. Divide by the smallest, 0.681. $\text{K} : \text{Cr} : \text{O} = 1.00 : 1.00 : 3.49$.

Step 3. Whole numbers. $3.49$ is close to $3.5$, so multiply all by $2$: $2 : 2 : 7$.