What is the largest square that can be used to fill a 63 by 28 rectangle?
A) 14 by 14
B) 63 by 63
C) 7 by 7
D) 28 by 28
E) 5 by 5

Question

What is the largest square that can be used to fill a 63 by 28 rectangle? ​
A) 14 by 14
B) 63 by 63
C) 7 by 7
D) 28 by 28
E) 5 by 5

Quizplus · Accepted Answer

To fill the rectangle with square tiles, we need to find the greatest common divisor (GCD) of 63 and 28. 
By the prime factorization method, we have:
63 = 3 × 3 × 7
28 = 2 × 2 × 7 
The common factor is 7, which means we can fit 7 columns of tiles across and 3 rows of tiles down. 
This gives us a square of side length 7, which is the largest square that can be used to fill the rectangle.

What Is the Largest Square That Can Be Used to Fill