A room is $26\text{ feet}$ long and $10\text{ feet}$ wide. If its floor is to be covered by square tiles, how many minimum number of tiles will be required?

To find the minimum number of square tiles needed to fully tile the room without cutting, the size of each tile must be maximized. The maximum side length of a square tile is the Highest Common Factor ($\text{HCF}$) of the room's dimensions.
Dimensions are $26\text{ ft}$ and $10\text{ ft}$.

$$\text{HCF}(26,10)=2\text{ ft}$$

So, each square tile has a size of $2\text{ ft}\times 2\text{ ft}$.

$$\text{Area of one tile}=2\times 2=4\text{ sq ft}$$

$$\text{Total Area of the floor}=26\times 10=260\text{ sq ft}$$

The minimum number of tiles required is:

$$\text{Number of tiles}=\frac{\text{Total Area}}{\text{Area of one tile}}=\frac{260}{4}=65$$