Each question gives two numbers and asks for the largest factor they share: the greatest common factor of 96 and 84 is 12. Every pair on the sheet has a genuine common factor - the answer is never 1.
That is a deliberate choice. Two numbers picked at random usually share nothing but 1, and a page of questions answered "1" teaches a student to guess rather than to look. These pairs are built around a shared factor, so the work of finding it is always work worth doing.
The largest number that divides into both. For 24 and 42, the common factors are 1, 2, 3 and 6, so the GCF is 6.
List the factors of each number and look for the largest that appears in both. With larger numbers it is quicker to break each into its prime factors and multiply the ones they share.
Because every pair here is built from a shared factor on purpose. Coprime pairs are a real case, but a sheet of them is a sheet about noticing there is nothing to find.
Simplifying fractions, mostly. Reducing 18/24 to 3/4 means dividing both by their GCF of 6, which is why this shows up right before fraction work in fifth and sixth grade.