Answer to Question #130028 in Combinatorics | Number Theory for sasis

Question

11. Maya is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use?

Answer 1

The side length of the square needs to divide both 16 and 24 evenly. The largest such integer is (by definition) the greatest common factor. A suitable number is the largest integer divisor of these numbers, that is, 8.

16 =4×4 or 8 × 2

24 =4×6 or 8 ×3

So largest square tile is 8

Answer: Maya can use the largest tile of dimension 8x8 inches.