Prime factors of 105488578125 are

3^9 x 5^6 x 7^3.

Since there are no powers of 2 here all the factors of this number will be odd.

The number of factors is given by the product of the highest exponent of each prime factors + 1.

In this case (9 + 1)×(6 + 1)×(3 + 1) = **280**.