Discussion
How many minimum number of square tiles are needed to cover a rectangular floor of dimension 5.25m and 5.10m completely?
Answer: A
Square tiles must fit a whole number of times along both edges, so the tile's side must divide both dimensions. Fewest tiles means largest tiles, so take the highest common factor.
\[ 5.25 \text{ m} = 525 \text{ cm}, \qquad 5.10 \text{ m} = 510 \text{ cm} \]
\[ 525 = 3 \times 5^{2} \times 7, \qquad 510 = 2 \times 3 \times 5 \times 17 \]
\[ \text{HCF} = 3 \times 5 = 15 \text{ cm} \]
\[ n = \frac{525}{15} \times \frac{510}{15} = 35 \times 34 = 1190 \]
Converting to centimetres first is essential - the highest common factor of 5.25 and 5.10 is not a whole number of metres.
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