  In this article, we derive lower bounds for the number of distinct prime
divisors of families of non-zero Fourier coefficients of non-CM primitive cusp
forms and more generally of non-CM primitive Hilbert cusp forms. In particular,
for the Ramanujan $\Delta$-function, we show that for any $\epsilon > 0$, there
exist infinitely many natural numbers $n$ such that $\tau(p^n)$ has at least $$
2^{(1-\epsilon) \frac{\log n}{\log\log n}} $$ distinct prime factors for almost
all primes $p$. This improves and refines the existing bounds. We also study
lower bounds for absolute norms of radicals of non-zero Fourier coefficients of
Modular forms alluded to above.
