There are 8 proper fractions with a denominator of 30 that are irreducible:
1/30, 7/30, 11/30, 13/30, 17/30, 19/30, 23/30, 29/30
We cannot count any even numerators, as 30 is even and would therefore make the fraction reducible.
We cannot count any numerators that are a multiple of 3, as it is a factor of 30. Likewise we cannot count any numerators that are a multiple of 5.
