Final answer:
Using the relationship between the product of two numbers and their HCF and LCM, none of the options provided (10, 20, 30, 40) is the correct HCF for two numbers with a product of 2,800 and LCM of 56 as the calculations reveal inconsistencies.
Step-by-step explanation:
The question asks us to find the Highest Common Factor (HCF) of two numbers given that their product is 2,800 and their Least Common Multiple (LCM) is 56. To determine the HCF, we can use the relationship between the product of two numbers, their LCM, and their HCF, which is:
Product of the numbers = LCM × HCF
By substituting the given values into this formula, we get:
2,800 = 56 × HCF
Next, we solve for HCF:
HCF = 2,800 / 56
HCF = 50
However, since 50 is not one of the provided options, we should review the calculation to ensure no mistakes have been made. On reviewing, we realize we made an error—the correct HCF computation should be:
HCF = 2,800 / 56
HCF = 50
Since 50 is not an option and we need to ensure we have not overlooked any factors, let's try option (b) 20 and check if it fits our product and LCM:
2,800 = LCM × HCF
2,800 = 56 × 20
Since 56 × 20 equals 1,120 and not 2,800, option (b) is incorrect. Continuing this process with different options, we find that option (d) is actually the correct answer:
2,800 = 56 × 40
As 56 × 40 equals 2,240 and not 2,800, there seems to be a mistake in the provided options and none of them are correct. After carefully verifying the calculations, it's clear that an error has been made in the question details or the provided options. The correct HCF with the given conditions does not match any of the available options.