Aptitude - Area - Discussion

@Tina.

The dimensions of the room is 1517cm X 902cm.
Square tiles of the same side are only to be used. So dimensions of the square tiles should not be in integral metres. Since no. of square tiles to be paved are whole numbers, 1517 and 902 should be divisible by a number which gives the number of square tiles to be paved along length and breadth.
Thus hcf is used.
Area of room / Area of 1 tile = No. of tiles.
= ( 1517 X 902 ) / ( 41 X 41 ) = 37 X 22 = 814 tiles.

Length and breath are given.

So area of rectangle is lxb.

Also they are askin to find the least no. of square tiles.

For square tiles we need the area.

In a square al the sides are equal.

Hcf is the highest common factor of 1517 and 902.

So 41 is the hcf n area of square is 41^2.

So divide area of rect by area of square.

902)1517(1
902
------
615)902(1
615
---
287)615(2
574
---
41)287(7
287
---
0

By this method of successful division, remainder goes 0. Last divisor forms your req. HCF....

So 41 is ur HCF :-)

HCF of any two or more numbers tells the highest possible no that can divide all the numbers. Since the question asks the minimum no of tiles, so it means you need a maximum possible size of the tile. Which will ensure minimum no of tiles?

If the question says that maximum tiles then you will calculate LCM.

Since hcf is a prime no. , how we can find the hcf of such big numbers.

For those who want to know why hcf::.

As we have to set square tiles in a rect. Floor that's why we need a comman factor for both length and breadth so that the no. Of tiles is a natural number but not a fraction!

We need that size of square which must occupy the entire space. If we take side of some other square, then 100% some space gona left as we can't bread the last tile. If we take the hcf, then we can get the side of square which is divisible by length and breadth both exactly.

The least number is asked that means a single tile with the maximum dimension.

For this try LCM , you will get the maximum number of tiles with minimum dimensions whereas, in HCF, you will get the largest dimension possible. So that only HCF is used to find the answer.

@Jhanvi.

In the question, one length is given in cm and another in m. So we have to convert m into cm.
i.e 15m=15 * 100cm (same for the breadth).

And for HCF.

1517 = 37 * 41,
902 = 22 * 41,

So HCF = 41,
Area = 41 * 41,
Req no of tiles = 1517 * 902/41 * 41 = 814.

Here 41 * 37=1517 and 41 * 22=902.

So, 41 comes in both the no. (which is called hcf).
Now the area of the floor is 1512 * 902.
So least no. of tiles to cover the floor = n * 41^2 (as square tile can be taken of length 41).
Therefore n =37*22 =814.

HCF is taken because we want the least no.of tiles in this question. If we want least no of tiles then we have to maximise the dimensions of tiles.

So HCF (Higher Common Factor) is used to maximise the dimensions of tiles.