The number of neutrons in an isotope can be found using the formula:
\[
\text{Neutrons} = \text{Mass number} - \text{Atomic number}
\]
For \(^{238}U\), the atomic number is 92, so:
\[
\text{Neutrons} = 238 - 92 = 146
\]
Thus, the correct answer is 146.