Final answer:
A coach cannot divide 43 students into equal groups, other than single groups of 1 or one large group of 43, since 43 is a prime number.
Step-by-step explanation:
The question posed is whether a coach can divide 43 students trying out for a basketball team into equal groups. To determine this, we look for factors of 43, which are only 1 and 43 itself because 43 is a prime number.
Therefore, the coach cannot separate the students into equal groups of any number other than 1 or 43. The groups would either have to be one large group of 43 or 43 groups of one student each, which would not constitute a team.