Introduction:
To determine whether it is possible to have two numbers whose highest common factor (HCF) is 18 and least common multiple (LCM) is 760, we need to understand the relationship between HCF and LCM. The HCF is the largest number that divides two or more numbers without leaving a remainder, while the LCM is the smallest multiple that is divisible by two or more numbers.

Understanding the HCF and LCM:
- HCF: The HCF of two numbers is always a divisor of both numbers. For example, if the HCF of two numbers is 18, it means that 18 is a common divisor of both numbers.
- LCM: The LCM of two numbers is always a multiple of both numbers. For example, if the LCM of two numbers is 760, it means that 760 is a common multiple of both numbers.

Relationship between HCF and LCM:
- The product of the HCF and LCM of two numbers is equal to the product of the two numbers. Mathematically, it can be represented as HCF * LCM = a * b (where a and b are the two numbers).
- If the HCF of two numbers is 18 and the LCM is 760, then 18 * 760 = a * b.

Analysis:
Let's analyze the factors of 760 and see if it is possible to find two numbers whose HCF is 18 and LCM is 760.

Factors of 760: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760.

Possible Scenarios:
1. One number is a multiple of 18 and the other number has no factor of 18:
- In this scenario, the number that is a multiple of 18 can have 18 as a factor, but the other number cannot have 18 as a factor. Therefore, it is not possible to have two numbers whose HCF is 18 and LCM is 760.

2. Both numbers have 18 as a factor:
- In this scenario, both numbers can have 18 as a common factor, but the LCM will not be 760. The LCM will be a multiple of 18, but it will not be exactly 760.

Conclusion:
Based on the analysis, it is not possible to have two numbers whose HCF is 18 and LCM is 760. The factors of 760 do not allow for such a combination.

We know that hcf of two numbers is always a divisor of lcm of those two numbers.Since 760 is not completely divisible by 18, therefore it is not possible to have two numbers whose hcf is 18 and lcm is 760.