Question

The dimensions of a window are 156 cm × 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Answer 1

We need to find H.C.F. (156, 216).

Prime factorization of 156:

156 = 2 × 78

= 2² × 39 

= 2² × 3 × 13

Prime factorization of 216:

216 = 2 × 108

= 2² × 54 

= 2³ × 27 

= 2³ × 3³

H.C.F. is the product of the lowest powers of common prime factors:

H.C.F. = 2² × 3

= 4 × 3 

= 12

Thus, the side length of the maximum square is 12 cm.

Finding the number of squares:

Number of squares = `"Area of window"/"Area of one square"`

Number of squares = `(156 xx 216)/(12 xx 12)`

Number of squares = `(156/12) xx (216/12)`

= 13 × 18

= 234

The maximum side length of the square is 12 cm and the total number of squares formed is 234.