Economists were left scratching their heads yesterday after the unemployment rate dropped to 9.0 percent — its lowest level in 21 months — while just 36,000 jobs were added to the US economy in January.

The new jobs, many of which were added in factories as that sector was growing at its best pace in nearly 13 years, were far fewer than Wall Street had expected — but it was enough to help cut the unemployment rate from 9.4 percent in December.

Of course, the fact that 504,000 people left the workforce also helped.

Nonetheless, the 36,000 jobs added highlight the slow, stubborn recovery and the years it will take to create the 8 million-plus jobs lost in the last three-plus years.

“Some see a dim light at the end of the tunnel as just an oncoming train,” said economist Dan Seiver, a finance professor at San Diego State University. “I see a busy economy ahead . . . making painfully slow progress.”

Indeed, government reports yesterday showed a split picture. While the 36,000 new jobs were disappointingly low, the jobless rate dipped more than anyone expected, to 9 percent. That resulted from 504,000 people giving up the search for work.

Economist Gary Burtless at the Brookings Institution said Uncle Sam’s report “offers a puzzling and mixed picture of the health of the current job market.”

What concerns many experts is the way the government counts the workforce.

Economists explained that severe weather across much of the US kept thousands of job-hunters indoors in recent weeks when they might have been pounding the pavement. As a result, they were counted by Labor Department poll takers as technically leaving the ranks of the unemployed.

“If a lot of people who are out of work aren’t counted anymore, then the unemployment rate goes down,” said Seiver.

But when people see new hiring, they start looking for work again and are counted as among the unemployed in search of jobs, he said.

“Even with the economy’s improvement ahead in February, it could cause the jobless rate to rise in February,” Seiver said.

Meanwhile, the report said that the number of people who called themselves self-employed rose by 165,000 to 9.7 million in January, the highest total since May. Retailers added 28,000 jobs, the largest number in a year, and factories added 49,000 jobs.

On the downside, restaurants and hotels cut 2,200 jobs, while governments eliminated 14,000 jobs and financial services trimmed 10,000.

“It is clear that the drop in unemployment reflected more jobs being added, not a drop in the labor force,” said economist Nigel Gault at IHS Global Insight, taking a contrarian view.

Harsh snowstorms blocked hiring of about 32,000 in construction industries and another 38,000 in transportation and warehousing, the report said. Experts expect the hiring to rise in February.

“We know the job market is recovering,” said economist Neil Dutta at Bank of America Merrill Lynch. tharp@nypost.com