The LCM and HCF of two numbers are equal and the product of two numbers is 1369. Find the HCF of the numbers.

Given that the LCM and HCF of two numbers are equal, it means that the two numbers are the same. This is because the LCM (Least Common Multiple) of two identical numbers is the number itself, and the HCF (Highest Common Factor) of two identical numbers is also the number itself.

We are also given that the product of the two numbers is 1369.

Let's denote the two numbers as 'a' and 'b'. Since the two numbers are the same, we can say that a = b.

The product of the two numbers is given by a * b = 1369.

Substituting b = a into the equation gives us a * a = 1369.

This simplifies to a^2 = 1369.

Taking the square root of both sides gives us a = sqrt(1369) = 37.

Therefore, the two numbers are 37 and 37, and the HCF of the numbers is 37.