Find the biggest square tile that covers a 12 ft by 16 ft floor exactly, and meet the Highest Common Factor (HCF).
Preview · progress not saved — Chapter 1 is free
A square tile fits a side exactly only if its length is a factor of that side.
For tiles to fit the 12 ft breadth with no gap, the side of the tile must be a factor of 12.
For tiles to fit the 16 ft length, the side must be a factor of 16.
Listing factors of 12 and 16 to pick the best tile.
Problem. Sameeksha's room is 12 ft by 16 ft. Which whole-number tile size uses the fewest square tiles? (Textbook pp. 47–48)
The Highest Common Factor is the greatest of the common factors.
Fill in how many 4 ft tiles cover the floor.
Textbook p. 48: how many 4 ft tiles should Sameeksha buy?
Along the 12 ft side: 12 ÷ 4 = tiles.
Along the 16 ft side: 16 ÷ 4 = tiles.
Total: 3 × 4 = tiles.
With 2 ft tiles instead, she would need 6 × 8 = tiles.
Quick tiling and common-factor questions.
Try This (p. 48): suppose a tile's side could be a fraction of a foot. Could Sameeksha use fewer tiles than with 4 ft tiles?