An interesting question

Q 1 A rectangular floor is 2016" " cm long and 1560" " cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

Ans To find the least number of square tiles needed to pave the rectangular floor, we need to find the side length of the largest square tile that can exactly measure both the length and breadth of the floor. In other words, we need to find the greatest common divisor (GCD) of the dimensions of the floor.

The dimensions of the floor are:

Length = 2016 cm

Breadth = 1560 cm

Let's find the GCD of 2016 and 1560:

GCD(2016, 1560) = 24

Now that we have the side length of the largest square tile that can exactly measure both dimensions of the floor, let's calculate the number of such tiles required to pave the floor. We can do this by dividing the area of the floor by the area of one tile:

Number of tiles = (Area of the floor) / (Area of one tile)

= (Length x Breadth) / (Side length of tile)^2

= (2016 x 1560) /$ (24^2)$

= (3144960) / (576)

= 5460

Therefore, the least possible number of square tiles required to pave the floor is 5460.Q 1 A rectangular floor is 2016" " cm long and 1560" " cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

Ans To find the least number of square tiles needed to pave the rectangular floor, we need to find the side length of the largest square tile that can exactly measure both the length and breadth of the floor. In other words, we need to find the greatest common divisor (GCD) of the dimensions of the floor.

The dimensions of the floor are:

Length = 2016 cm

Breadth = 1560 cm

Let's find the GCD of 2016 and 1560:

GCD(2016, 1560) = 24

Now that we have the side length of the largest square tile that can exactly measure both dimensions of the floor, let's calculate the number of such tiles required to pave the floor. We can do this by dividing the area of the floor by the area of one tile:

Number of tiles = (Area of the floor) / (Area of one tile)

= (Length x Breadth) / (Side length of tile)^2

= (2016 x 1560) /$ (24^2)$

= (3144960) / (576)

= 5460

Therefore, the least possible number of square tiles required to pave the floor is 5460.