Find the least number of square tiles which can the floor of a rectangular shape having length and breadth 16 meters 58 centimeters and 8 meters 32.

Firstly, we find the length of the largest tile so for that we have to find the HCF of 1658 and 832.

Here, 1658 > 832

So, we divide 1658 by 832

By using Euclid’s division lemma, we get

1658 = 832 × 1 + 826

Here, r = 826 ≠ 0.

On taking 832 as dividend and 826 as the divisor and we apply Euclid’s division lemma, we get

832 = 826 × 1 + 6

Here, r = 6 ≠ 0

So, on taking 826 as dividend and 6 as the divisor and again we apply Euclid’s division lemma, we get

826 = 6 × 137 + 4

Here, r = 4 ≠ 0

So, on taking 6 as dividend and 4 as the divisor and again we apply Euclid’s division lemma, we get

6 = 4 × 1 + 2

Here, r = 2 ≠ 0

So, on taking 4 as dividend and 2 as the divisor and again we apply Euclid’s division lemma, we get

4 = 2 × 2 + 0

The remainder has now become 0, so our procedure stops. Since the divisor at this last stage is 79, the HCF of 1658 and 832 is 2.

So, the length of the largest tile is 2 cm

Area of each tile = 2 × 2 = 4cm²

The required number of tiles =

=

= 344864

Least number of square tiles are required are 344864