Question

A rectangular floor has dimensions 28 units by 21 units, and needs to be covered by identical square tiles. What’s the maximum length of the square tile that can evenly cover the entire floor?

• A. $1\text{unit}$
• B. $3\text{units}$
• C. $7\text{units}$
• D. $21\text{units}$

Answer 1

The correct option is C $7\text{units}$

The rectangular floor can be covered with square tiles with the longest edge lengths possible.

The maximum edge length should be the greatest common factor of both the length and the width of the rectangular sheet.

Find the GCF of 21 and 28 by the prime factorization method:
$21=3\times 728=2\times 2\times 7$
Here, the greatest common divisor of the two numbers is $7.$

Thus, the maximum length of the square tile that can evenly cover the entire floor is $7\text{units}$