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?​

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:

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

Answer 2

GIVEN :-

• Anirudh wants to cut a large rectangular board into small identical square pieces.

• The size of the board = 18 inches by 30 inches

TO FIND :

• The least number of square pieces he can cut without wasting any of the board = ?

KNOWLEDGE REQUIRED :

• To find the least number of square pieces Anirudh can cut without wasting any of the board, we need the highest common factor (HCF) of 18 and 30.

SOLUTION :

⇰ Factors of 18 = 1, 2, 3, 6, 9 and 18

⇰ Factors of 30 = 1, 2, 3, 6, 15, 30

ஃ HCF of 18 and 30 = 6

ANSWER :

• Thus he can cut the board into 6-inch square pieces without wasting any of the board since 6 divides into both 18 and 30 and is the largest number that does so.

The least number of squares that he can cut :-

• Area of the board / Area of the square

= (18 × 30) / (6 × 6)

= 15