One natural number is 3 more than another, and their product is 180. Find these natural numbers.

Let x be one of the given natural numbers, then (x + 3) is the second natural number.

x * (x + 3) is their product, which is 180.

Hence, x * (x + 3) = 180.

Let’s solve the equation:

x ^ 2 + 3x – 180 = 0.

Let’s calculate the discriminant:

D = 3 ^ 2 – 4 * 1 * (-180) = 9 + 720 = 729.

Then x1 = (-3 + √729) / (2 * 1);

x1 = (-3 + 27) / 2;

x1 = 12;

x2 = (-3 – √729) / (2 * 1);

x2 = (-3 – 27) / 2;

x2 = -15.

x = -15 is not a natural number.

Therefore, x = 12 is one natural number.

Let’s find the second:

12 + 3 = 15.

Answer: 12 and 15.