Question

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

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Consider the 3 consecutive numbers 2, 3, 4

`(2 xx 3 xx 4)/6 = 24/6` = 4

Now, consider another 3 consecutive numbers 4, 5, 6

`(4 xx 5 xx 6)/6 = 120/6` = 20

Now, consider another 3 consecutive numbers 7, 8, 9

`(7 xx 8 xx 9)/6 = 504/6` = 84

Hence, the statement “product of three consecutive positive integers is divisible by 6” is true.