If a company issues 2,500,000 shares with voting rights how many shares must an investor by to be assured control of the company

I think for an investor to have control of a company, he/she needs 51% of the voting rights...

51% of 2,500,000 = 0.51(2,500,000) = 1,275,000 <==

To become a major investor (which is to have an assured amount of control of the company) you must have ~20 -25% of the shares.

That is 500,000 - 625,000 shares in the company

hope this helps