Fast prime factorization of n factorial

[eightnoteight]

i'm solving EASYFACT problem; but i'm getting TLE, i don't know any fast method of prime factorization of n factorial
i'm solving using the usual method (complexity: klogk where k is the number of primes under n)

        result = 1
        for (int32_t x = 1, pxcount = 0; primes[x] <= n; ++x, pxcount = 0) {
            for (int32_t y = primes[x]; y <= n; y *= primes[x])
                pxcount += n / y;
            result = (1ll * result * (pxcount + 1)) % m;
        }

what should i do to solve this problem.. please help me; thanks

[luckymastermin]

Yes, There is much faster way to do this, you can reduce this to sqrt(n).
try to observe the pattern in divisors of factorial.