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Show that the product of any two consecutive positive integers is always even

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Prove that out of any two consecutive positive integers one and only one is even

Find two consecutive positive even integers whose product is 288.

Q. Prove that the product of any three consecutive positive integers is divisible by 6.

Q. State true or false.
(i) The product of a negative and a positive integer may be zero.
(ii) The product of two negative integers is always positive.
(iii) The product of two integers with opposite signs is the same as the product of their absolute values.
(iv) If exactly one of the three given integers is negative, then product is always negative.
(v) The product of any two positive or any two negative integers is always smaller than the integers.

1. Prove that the product of two consecutive positive integers is divisible by 2.

2. Prove that the product of three consecutive integers is divisible by 6.

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