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

While there is no minimum order limit on the purchase of a publicly traded company's stock, it's advisable to buy blocks of stock with a minimum value of $500 to $1,000. This is because no matter what online or offline service an investor uses to purchase stock, there are brokerage fees and commissions on the trade.

When purchasing stock in the open market, an investor should open a trading or brokerage account with a leading financial institution such as eTrade, Charles Schwab or Ameritrade. Once the investor opens a trading account, it's up to him how many stocks he wants to purchase at any one time. Before making any purchase decisions, an investor should do ample research on the various types of equity securities that are offered. Once an investor identifies a stock worth purchasing, he should execute an online trade by using his brokerage account. There are two types of trades that can be made in this scenario: a market order and a limit order.

If the investor makes a market order, he chooses to purchase the stock at the current market price. If the investor makes a limit order, he chooses to wait to purchase the stock until the price falls to a specific limit. While purchasing a single share isn't advisable, if an investor would like to purchase one share, he should try to place a limit order so he has a greater chance of capital gains that offset the brokerage fees.

However, 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.

A DRIP 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. Thus, 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. (For related reading, check out The Perks of Dividend Reinvestment Plans.)

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, fractional shares are also likely to increase in popularity.