Use the quadratic equation to solve this problem. Because these two numbers are consecutive numbers, so if the first number is x, then he second number is (x + 1). Because the product of the two consecutive number is 240, so x(x + 1) = 240. Then x2 + x = 240. Since the equation is two degrees of the variable x, so move the number 240 to the left side of the equation. We get the quadratic equation: x2 + x - 240 = 0. The left side of the equation can be factored as (x - 15)(x + 16) = 0. Then (x - 15) = 0 or (x - 16) = 0. Thus, we get two solutions x1 = 15 and x2 = 16. So, these two consecutive numbers are 15 and 16.