The product of two numbers is 1296.

Let the two numbers be a and b.

From the first statement, we have:

a x b = 1296

If one number is 16 times the other, then we have:

b = 16 x a.

Substituting this value in the first equation, we get:

a x (16 x a) = 1296

By simplifying both sides, we get:

a2 = 1296/16 = 81

Hence, a is the square root of 81, which is 9.

To find b, use equation b = 16 x a.

Since a = 9:

b = 16 x 9 = 144

So, the two numbers satisfying the question are 9 and 144.