Difference between perfect square and a number that can be expressed as product of consecutive integers:

By Ali Khan -


A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer¹. For example, 1, 4, 9, and 16 are perfect squares because they are the squares of 1, 2, 3, and 4 respectively. A perfect square can also be written as x^2, where x is an integer.


A number that can be expressed as a product of consecutive integers is a number that can be obtained by multiplying two or more integers that follow each other in order. For example, 6, 24, and 120 are numbers that can be expressed as products of consecutive integers because they are equal to 2 x 3, 2 x 3 x 4, and 2 x 3 x 4 x 5 respectively. A number that can be expressed as a product of consecutive integers can also be written as x(x + 1)(x + 2)...(x + n), where x and n are integers.


The difference between a perfect square and a number that can be expressed as a product of consecutive integers is that a perfect square has only one factor pair that consists of the same integer, while a number that can be expressed as a product of consecutive integers has multiple factor pairs that consist of different integers. For example, 16 is a perfect square because it has only one factor pair that is 4 x 4, while 24 is a number that can be expressed as a product of consecutive integers because it has multiple factor pairs that are 2 x 12, 3 x 8, and 4 x 6.



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