Consider four base ten positive integers 42⁹⁸, 70⁷⁰, 105⁴² and 154²⁸ – and, determine the total number of positive integers dividing:

(I) At least one of the four given numbers.

(II) At least two of the four given numbers.

(III) At least three of the four given numbers.

(IV) Each of the four given numbers.