"The product of three consecutive positive in | vedclass

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(A) Let the three consecutive positive integers be $n, (n + 1),$ and $(n + 2).$In any set of two consecutive integers,one must be even (divisible by $

Vedclass · Accepted Answer

True

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(A) Let the three consecutive positive integers be $n, (n + 1),$ and $(n + 2).$In any set of two consecutive integers,one must be even (divisible by $2$). Therefore,in any set of three consecutive integers,at least one must be divisible by $2$.In any set of three consecutive integers,one must be a multiple of $3$ (divisible by $3$).Since the product is divisible by both $2$ and $3$,and $2$ and $3$ are coprime (their greatest common divisor is $1$),the product must be divisible by their product,which is $2 	imes 3 = 6$.Thus,the statement is true.

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

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