Question

Anirudh wants to cut a large rectangular board into small identical square pieces. If the board size is 18 inches by 30 inches,
What is the least number of square pieces he can cut without wasting any of the board?

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Answer 1

$\LARGE{ \underline{ \bf{Required \: answer:}}}$

If we want to cut the rectangular board into square pieces that actually means that Anirudh needs to cut pieces that are equal in length and width. (In form of squares)

“Without wasting any of the board” means that he needs to choose a side length that divides evenly into both 18 and 30. And that is the common factor of 18 and 30.

“The least number of square pieces” means that he needs to choose the largest possible squares length of the side of the square.

Hence,

HCF of 18 and 30

18 = 2 × 3²

30 = 2 × 3 × 5

• HCF of 18 and 30 is 6

If the side length is 6 m, then the width 18 m can be divided 3 times and the length 30 m can be divided 5 times.

Thus,

The least number of square pieces he can cut without wasting any of the board is:

$\huge{ \boxed{ \purple{3 \times 5 = 15}}}$

Answer 2

Area of Rectangle = 18 * 30 = 2*3*3 * 3*2*5 = 2^2 * 3^2 * 15

Area of individual square of side s= s^2.

Number of such squares = n

so, ns^2 = 2^2 * 3^2 * 15

s^2 can be 2^2*3^2. 15 remains on one side. This is number of squares n.

Is this logic correct? :?