General Motors Company (NYSE:GM) is one step closer to getting American taxpayers out of its business, but the largest U.S. carmaker still owes them billions and recovering the money will be very unlikely based solely on the sale of GM shares held by the U.S. Treasury.

The Treasury Department said it sold $876.9 million worth of GM shares in July. Based on last month’s highest and lowest prices, the government sold between 23 million and 27 million shares.

“As of July 31, 2013, Treasury has recovered approximately $34.6 billion of its investment in GM through repayments, sales of stock,  dividends, interest, and other income,” the Treasury said on Monday in its monthly report to Congress. Under the Trouble Asset Relief Program, the government bailed out banks and auto makers GM and Chrysler following the 2009 subprime mortgage meltdown.

The government initially invested $51 billion to “stabilize and restructure GM.” Based on this latest report, taxpayers are owed $16.4 billion of the principal bailout sum before they can break even.

A phone call on Tuesday to the Treasury seeking the current number of shares held by the government yielded a "no comment." Yet, back-of-the envelope calculations suggest that GM’s share price would have to more than double for the government to recover its investment solely from selling the shares it holds as of today.

So how many shares do taxpayers own in GM through the TARP bailout? About 187 million shares.

Before April, the government owned 300.1 million shares. That dropped to 241.7 million shares after the Treasury sold 58.4 million shares for $1.6 billion in a trading plan that ended April 11.

In June the Treasury sold an additional 30 million shares, raising a billion dollars and dropping its stake to 211.7 million shares.

Assuming the Treasury sold 25 million shares in July to raise the $876.9 million, then the current stake is about 187 million shares.

The Treasury said in December it wanted to be fully divested by the end of the first quarter of 2014, “subject to market conditions.” Based on selling 187 million GM shares, at Monday’s closing price of $35.98, the government would raise about $6.73 billion, leaving it with nearly $10 billion still owed to it with no stock left to sell.

To raise the $16.4 billion that would allow the federal government to say it broke even on the GM bailout, it would have to sell 187 million shares at about $87 apiece. Last week, GM Chief Financial Officer Dan Ammann told Reuters that the company had no current plans to please investors by starting to pay dividends on its common shares.

The company currently pays a dividend on preferred shares, and it reported $1.2 billion in net profit in the second quarter.