Question

455 What is the minimum number of square marbles required to tile a floor of length 6 meter 24

cm. and width 4 meter 16 cm?
A. 6
B. 12
C. 14
D. 8​

Answer 1

6

Explanation:

Length of a floor, l = 6 m 24 cm = 624 cm

Breadth of a floor, b = 4 m 16 cm = 416 cm

We need to find the minimum number of square marbles required to tile the floor.

Taking factors of 624 and 416 by prime factorization :

624 = 2 x 2 x 2 x 2 x 3 x 13

416 = 2 x 2 x 2 x 2 x 2 x 13

Their HCF = 208

No of tiles length wise = 624/208 = 3

No of tiles width wise = 416/208 = 2

The minumum no of tiles needed = 3 × 2 = 6

Hence, 6 square tiles are required to tile a floor.