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  • The product of three consecutive positive integers is divisible by 6”. Is this statement true or falseJustify your answer

The product of three consecutive positive integers is divisible by 6”. Is this statement true or false? Justify your answer

Answers (1)

The given statement is true in all the conditions.
  Let three consecutive positive integers be, x, x + 1 and x + 2.
Divisibility by 3: Whenever a number is divided by 3, the remainder obtained is either 0 or 1 or 2.
\thereforen = 3p or 3p + 1 or 3p + 2, where p is some integer.
So, we can say that one of the numbers among x, x + 1 and x + 2 is always divisible by 3.

\Rightarrow x (x + 1) (x + 2) is divisible by 3.
Divisibility by 2: Whenever a number is divided 2, the remainder obtained is 0 or 1.
\thereforen = 2q or 2q + 1, where q is some integer.
So, we can say that one of the numbers among x, x + 1 and x + 2 is always divisible by 2.
\Rightarrowx (x + 1) (x + 2) is divisible by 2.
Since, x (x + 1) (x + 2) is divisible by 2 and 3.
   \therefore x (x + 1) (x + 2) is divisible by 6.

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