A room is 750 cm long and 525 cm wide. Its floor is to be paved with square tiles. What is the least number of tiles required?

Correct option is A

Given:

Length of the room = 750 cm

Width of the room = 525 cm

We are to find the least number of square tiles needed to pave the floor

Concept Used:

To use the least number of square tiles, the side of each square tile should be the greatest common divisor (HCF) of the room’s length and width

Number of tiles = $$\frac{\text{Area of floor}}{\text{Area of one tile}} = \frac{\text{Length} \times \text{Width}}{\text{(HCF)}^2}$$​​

Solution:

HCF of 750 and 525

Prime factors of 750 = $$2 \times 3 \times 5^3$$​​

Prime factors of 525 = $$3 \times 5^2 \times 7$$​​

HCF = $$3 \times 5^2 = 75$$​​

Now,

Number of tiles = $$\frac{750 \times 525}{75^2} = \frac{393750}{5625} = 70$$​​