Discussion

What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?

Answer: C

Square tiles must divide both dimensions exactly, and the fewest tiles means the largest tile - the highest common factor.

\[ 15 \text{ m } 17 \text{ cm} = 1517 \text{ cm}, \qquad 9 \text{ m } 2 \text{ cm} = 902 \text{ cm} \]

\[ 1517 = 37 \times 41, \qquad 902 = 2 \times 11 \times 41 \]

\[ \text{HCF} = 41 \text{ cm} \]

\[ n = \frac{1517}{41} \times \frac{902}{41} = 37 \times 22 = 814 \]

The awkward 17 cm and 2 cm are deliberate: they force a common factor of 41 rather than a round number.

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