To solve the problem where the highest common factor (HCF) of two numbers is 16 and their least common multiple (LCM) is 160, and one of the numbers is given as 32, we use the relationship:

$\text{HCF} \times \text{LCM} = \text{Product of the numbers}$

Given:

• HCF = 16
• LCM = 160
• One number = 32

Let the other number be $y$. Using the formula:

$16 \times 160 = 32 \times y$

$2560 = 32 \times y$

Now, solve for $y$:

$y = \frac{2560}{32} = 80$

So, the other number is 80.

Do you need more details on this or have any other questions? Here are some related queries you might find interesting:

1. How does the relationship between HCF and LCM help in solving problems involving more than two numbers?
2. What are the properties of HCF and LCM when dealing with algebraic expressions?
3. Can we find the HCF and LCM of more than two numbers? If so, how?
4. How would this problem change if the HCF was different?
5. What are some real-life applications of HCF and LCM?

Tip: Always verify your calculations, especially in problems involving ratios or fractions, as simple arithmetic errors can lead to incorrect conclusions.