To find the Highest Common Factor (HCF) of 60, 24, 18, and 96, we can follow these steps using the method of prime factorization:

1. Prime factorization of 60: $60 = 2^2 \times 3 \times 5$

2. Prime factorization of 24: $24 = 2^3 \times 3$

3. Prime factorization of 18: $18 = 2 \times 3^2$

4. Prime factorization of 96: $96 = 2^5 \times 3$

Now, to find the HCF, we look for the lowest powers of the common prime factors between all numbers.

• The common prime factors are $2$ and $3$.
• For $2$, the lowest power is $2^1$ (appearing in 18).
• For $3$, the lowest power is $3^1$ (appearing in 60, 24, 96).

Thus, the HCF is: $HCF = 2^1 \times 3^1 = 2 \times 3 = 6$

So, the HCF of 60, 24, 18, and 96 is 6.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you find the Least Common Multiple (LCM) of these numbers?
2. Can you explain the Euclidean algorithm for finding HCF?
3. What is the HCF of two numbers if one is a multiple of the other?
4. How do prime factorizations help in finding both HCF and LCM?
5. What is the relationship between HCF and LCM for two numbers?

Tip: To quickly check if a number is divisible by 6, ensure it is divisible by both 2 and 3.