NCERT Solutions for Class 7th Maths Chapter 3 In-text Questions — The Greatest of All
Book page 47 Updated on2026-09-19
Q1.
Sameeksha is building her new house. The main room of the house is 12 ft by 16 ft. She feels that the room would look nice if the floor is covered with square tiles of the same size. She also wants to use as few tiles as possible, and for the length of the tile to be a whole number of feet. What size tiles should she buy?
Answer
She should buy square tiles of side 4 ft.
The tiles must fit the room exactly, with no cutting.
Across the breadth: the side of the tile must be a factor of 12
Along the length: the side of the tile must be a factor of 16
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 16 = 1, 2, 4, 8, 16
Common factors = 1, 2, 4
Largest common factor = 4
So the possible tile sizes are 1 ft, 2 ft and 4 ft. The largest of these is 4 ft.
The 12 ft × 16 ft floor covered by 4 ft tiles — 3 rows of 4 tiles, 12 tiles in all, with nothing left over.
Why it happens: a tile of side s fits the 12 ft breadth only if 12 is a whole number of tiles, that is, only if s divides 12. The same argument along the length forces s to divide 16. So s has to be a common factor. Bigger tiles cover more floor each, so the fewest tiles come from the biggest common factor — the HCF.
Tip: 4 is the Highest Common Factor (HCF) of 12 and 16. It is also called the Greatest Common Divisor (GCD).
Q2.
So, the square tiles can have sides 1 ft, 2 ft, and 4 ft. Among these, she should use the largest sized square tile. Can you explain why?
Answer
Because a bigger tile covers more floor, so fewer tiles are needed.
Area of the room = 12 × 16 = 192 sq ft
With 1 ft tiles: 192 ÷ 1 = 192 tiles
With 2 ft tiles: 192 ÷ 4 = 48 tiles
With 4 ft tiles: 192 ÷ 16 = 12 tiles
Sameeksha wants as few tiles as possible, so she picks the 4 ft tile.
Why it happens: the floor area is fixed at 192 sq ft. A tile of side s covers s × s sq ft, so the number of tiles is 192 ÷ s². Making s as large as possible makes s² as large as possible, and so the count as small as possible.