A rectangular surface has length 4661 meters and breadth 3318 meters. On this area, square tiles are to be put. Find the maximum length of such tiles.

Given length and breadth are 4661 m and 3318 m respectively.

Here, 4661 > 3318

So, we divide 4661 by 3318

By using Euclid’s division lemma, we get

4661 = 3318 × 1 + 1343

Here, r = 1343 ≠ 0.

On taking 3318 as dividend and 1343 as the divisor and we apply Euclid’s division lemma, we get

3318 = 1343 × 2 + 632

Here, r = 632 ≠ 0

So, on taking 1343 as dividend and 632 as the divisor and again we apply Euclid’s division lemma, we get

1343 = 632 × 2 + 79

Here, r = 79 ≠ 0

So, on taking 632 as dividend and 79 as the divisor and again we apply Euclid’s division lemma, we get

632 = 79 × 8 + 0

The remainder has now become 0, so our procedure stops. Since the divisor at this last stage is 79, the HCF of 3318 and 4661 is 79.

Hence, the maximum length of such tiles is 79 meters.