Arectangular game board measures 126 centimeters by 90 centimeters. the game board is divided into small squares of equal size.
a. find the longest possible length of the side of one of the squares. (hint: use prime factorization)

Let’s simplify the situation:
The area of a game board is 126 centimetres by 90cm.

To get the total area let’s multiply:
a = L2 x W2
A= 1262 x 902
A = 11340 cm 2

Now we have the total area of the game board, next is to find the small squares inside the rectangle.

Let’s use prime numbers:
11340 | 2
5670 | 2
2835 | 5
567 | 3
189 | 3
63 | 3
21 | 3
7 | 7
1
=> 11340 = 2^2 x 3^4 x 5 x 7 = 2 ^ 2 x (3^2) ^ 2x5x7 = 18 ^ 2 x 5 x

Thus, the side length is 18 and we will have small squares all in all.