Number Theory : HCF, GCD, Factors, Divisors

Word problem in number theory, using the concept of HCF / GCD

Question

What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?

1. 176
2. 187
3. 54043
4. 748
   

Correct Choice is (2) and correct answer is 187

Explanatory Answer

The marbles used to tile the floor are square marbles. Therefore, the length of the marble = width of the marble.
As we have to use whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 74. And it should be the highest factor of 5 m 78 cm and 3m 74.

5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm.
The HCF of 578 and 374 = 34.

Hence, the side of the square is 34.

The number of such square marbles required = = 187 marbles.

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