Question

Which numbers can be represented by the most rectangles? What kind of numbers are they?

a) Prime numbers

b) Perfect squares

c) Odd numbers

d) Even numbers

Answer 1

Perfect squares are numbers that can be expressed as the product of an integer with itself and can be represented by the most rectangles due to their equal pair factors(option b).

Step-by-step explanation:

Numbers that can be represented by the most rectangles are option b: perfect squares.

Perfect squares, like 1, 4, 9, 16, and so on, are numbers that can be expressed as the product of an integer with itself. Since factors of perfect squares come in pairs that are identical (e.g., 3 x 3 for 9), they can be arranged to form a square, i.e., a rectangle with equal sides. Consequently, perfect squares have the most rectangle representations. For instance, the number 16 can be represented by rectangles of dimensions 1x16, 2x8, and 4x4.