Relative Primality
How many numbers between 1 and 3780 (inclusive) are relatively prime to 3780?
\(3780 = 2^2 \cdot 3^3 \cdot 5 \cdot 7\), so using the formula for Euler's \(\Phi\) function, there are
\((4-2) \cdot (27-9) \cdot (5-1) \cdot (7-1) = 864\) such numbers.