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)

The area of your game board is = 126 * 90 = 11340 cm^2;
A small suares has x^2 his area; where x measure his length;

Prime factorization

11340 | 2
 5670 | 2
 2835 | 5
  567  | 3
  189 | 3
    63 | 3
    21 | 3
      7 | 7
      1

11340 = 2^2 * 3^4 * 5 * 7 = 2^2 * ( 3^2 ) ^ 2 * 5 * 7 = 18^2 * 5 * 7

We observ that the possible length of the side is 18( we have 35 small squares ).