The Highest Common Factor of two numbers is (2/5)th of their Least Common…

To find the Highest Common Factor (HCF) of the two numbers, we can use the fundamental relationship between HCF, Least Common Multiple (LCM), and the product of two numbers.

Step-by-Step Calculation
Define the variables and relationships:

Let the HCF be h and the LCM be l.

The problem states that the HCF is (2/5) of the LCM: h = (2/5) * l

This also means: l = (5/2) * h = 2.5 * h

We know the fundamental property: Product of two numbers = HCF * LCM

Given: Product = 1,690

Set up the equation:

Substituting the relationship into the product property:
h * (2.5 * h) = 1,690
2.5 * h² = 1,690

Solve for h (HCF):

h² = 1,690 / 2.5

h² = 676

h = √676

h = 26