HCF and Floor Paving

Length $= 1591$ cm, Breadth $= 946$ cm. To minimize tiles, side of square tile must be HCF($1591, 946$). $1591 = 43 \times 37$ $946 = 43 \times 22$ $\text{HCF} = 43$ cm.

Least number of tiles $= \frac{1591 \times 946}{43 \times 43} = 37 \times 22 = 814$.