Explanation:

Certainly! Let's break down the problem to understand it:

- The numbers are in the ratio of 1:3:7. Let's assume the numbers are x, 3x, and 7x.

- Given, the LCM (Least Common Multiple) of these numbers is 336.

- For numbers in the form of ax, bx, cx, the LCM is determined by taking the greatest terms of each prime factor present when written in their simplest form.

- The LCM of x, 3x, and 7x is $21x$ (since 3 and 7 are co-prime factors). Thus, $21x=336$.

- Solving for x, you get $x=16$.

- Therefore, the numbers are 16, 48, 112.

- The Highest Common Factor (HCF) is x, which is 16.

- Among the options, the only suitable HCF is:

- Option 1: 16

- The correct answer is 16.

- .