Which method would you use to find the highest common factor using prime factors?

To find the highest common factor (HCF) using prime factors, listing all prime factors that appear in both numbers and then multiplying them is a systematic and effective approach.

Start by determining the prime factorization of each number. For example, if you have two numbers, you would break each number down into its prime factors. Once the prime factors are identified, you look for the factors that are common to both sets of prime factors. The HCF is obtained by multiplying these shared prime factors together.

This method works because the HCF is defined as the largest number that can divide both numbers without leaving a remainder, which corresponds directly to the multiplicative combination of their common prime factors.

The other methods listed do not properly correspond to finding the highest common factor. For instance, finding the greatest multiple of either number does not relate to factors and would not always yield the correct HCF. Summing the prime factors does not take into account the need for commonality, and multiplying both numbers together will give a product, not a factor. Thus, the most accurate and direct method in this context is to list and multiply the common prime factors.