Tutoring math, these definitions don’t come up often enough. The math tutor offers this brief read on them.

A factor of a number divides into it with no remainder.  For example, 5 is a factor of 15; 7 is a factor of 56.

A prime number has exactly two factors:  1 and itself.  Notice that 2 is prime, having only 1 and 2 as factors.  7 is also prime.  9 is not prime, since it has three factors:  1, 3, and 9 all divide into it with no remainder.  10 is not prime either.  1 is not prime, since it only has one factor:  1.

Numbers that are relatively prime don’t have to be prime, but they share no common factor except for 1.  12 and 5 are relatively prime, for instance.  10 and 15 are not relatively prime, since they have 5 as a common factor.

An application of relatively prime numbers is fraction reduction.  If the numerator (the top number) and the denominator (the bottom number) are relatively prime, the fraction is reduced.  Reduced might also be referred to as in lowest terms.

By that rationale, ²⁴⁄₁₈ is not in lowest terms because 24 and 18 are not relatively prime.   In particular, they share the common factor 6.  Dividing 6 out of both, we get ⁴⁄₃. Since 4 and 3 are relatively prime, the fraction is now reduced.

Hope this helps:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.