Many people would say the smallest number of shares that an investor can purchase is one, but the real answer is not as straightforward. 

The answer to this question is complicated further by something known as fractional shares. A fractional share is a share of equity that is less than one full share and usually is the result of a stock split, dividend reinvestment plan (DRIP), or similar corporate action.

Dividend Reinvestment Plan and Fractional Shares

A dividend reinvestment plan is a plan in which a dividend-offering corporation or brokerage firm allows investors to use dividend payouts to purchase more of the same shares. As this amount "drips" back into the purchase of more shares, it is not limited to whole shares.

In essence, you are not restricted to buying a minimum of one share, and the corporation or brokerage keeps accurate records of ownership percentages. For example, if you were enrolled into the DRIP of Cory's Tequila Corporation (CTC) and you owned one share of CTC—which pays a dividend of $2 per share and is trading at $40—the $2 dividend would be automatically used to purchase 0.05 ($2/$40) shares of CTC.

The reason DRIPs are so popular is that most of them don't have commissions or brokerage fees, so it is cheaper for investors to increase their holdings and use their dividend payouts without having to pay extra fees.

Fractional shares are also being utilized by investment companies and apps such as Betterment, Stash, and Stockpile. By allowing people to trade fractional shares, such companies provide investors, many of them beginners, with access to stocks they may otherwise not have been able to afford to trade. Due to the growing popularity of such investment platforms with both individual investors and roboadvisors, fractional shares will continue to grow in popularity.