A hall floor measures 6.24 m by 4.32 m. It is to be covered with identical square tiles without cutting any tile. What is the side of the largest such tile?

Explanation

1. 01

   Convert to cm: 624 cm and 432 cm.

2. 02

   The tile side must divide both, so take HCF(624, 432).

3. 03

   $624 = 2^4 \times 3 \times 13$, $432 = 2^4 \times 3^3$, so HCF = $2^4 \times 3 = 48$ cm.