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Question

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

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Solution

Given length and breadth are 4661m and 3318m respectively.
Here, 4661>3318
So, we divide 4661 by 3318.
By using Euclid's division lemma, we get
4661=33181+1343
Here, r=13430
On taking 3318 as dividend and 1343 as the divisor and we apply Euclid's division lemma, we get
3318=13432+632
Here, r=6320
So, on taking 1343 as dividend and 632 as the divisor and again we apply Euclid's division lemma, we get
1343=6322+79
Here, r=790
So, on taking 632 as dividend and 79 as the divisor and again we apply Euclid's division lemma, we get
632=798+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.

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