For an element represented as $_{Z}^{A}\text{X}$, $Z$ represents the atomic number and $A$ represents the mass number.

1. Atomic Number ($Z$): This is equal to the number of protons. For Lutetium ($^{175}_{71}\text{Lu}$), $Z = 71$. Therefore, the number of protons is 71.
2. Electrons: In a neutral atom, the number of electrons is equal to the number of protons. Thus, the number of electrons is 71.
3. Mass Number ($A$): This is the sum of protons and neutrons ($A = p + n$). Here, $A = 175$.
4. Neutrons ($n$): The number of neutrons is calculated as $A - Z = 175 - 71 = 104$.

Hence, the number of protons, neutrons, and electrons are 71, 104, and 71, respectively , , .