Rosa 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?

Please show working

8" by 8"

Six of those will fit on the board

Step-by-step explanation:

The largest tile she can use is a 8 inches by 8 inches tile.

Step-by-step explanation:

Rosa is making a game board that is 16 inches by 24 inches.

She wants to use square tiles.

The area of the game board (area of  a rectangle) is equal to length times width.

∴ Area = 16 inches × 24 inches = 384 square inches

The prime factors of 384 are; 2^7 × 3

We can put it as;

2^6 × 6 = 384

The square root of 2^6 is 2^3 = 8

So Rosa will need six square tiles of 8 inches by 8 inches each.

Hence the largest tile she can use is a 8 inches by 8 inches tile.