Given that the product of two consecutive numbers is 182.

Let us assume that the first number is x.

Then, the next number will be x+1.

We will rewrite the product of both numbers.

==> x*(x+1) = 182

Let us open the brackets.

==> x^2 + x = 182

==> x^2 + x - 182 = 0

Now we have a quadratic equation, we will use the formula to find the roots.

==> x1= ( -1 + sqrt(1+4*182) / 2

=(-1 + 27) /2

= 26/2 = 13

==> x1= 13

==> x2= (-1-27)/2 = -28/2 = -14

==> x2= -14

Then the numbers are:

**13 and 14 OR -13 and -14.**

We assume that x and x+1 are the two consecutive numbers whose product is 182.

So x(x+1) = 182.

We subtract 182 from both sides:

=> x^2+x -182 = 0.

=> (x-13)(x+14) = 0.

=> x-13 = 0, or x+14 = 0.

=> x= 13, or x= -14.

Therefore 13 and 14 are the two positive consecutive integers whose product is 182.

If you consider the consecutive negative numbers, then -14 and -13 are also the two consecutive numbers whose product is 182.