L.A. County’s unemployment rate rose slightly to 5.1 percent in October even as the number of payroll jobs reached 4.4 million for the first time ever, state figures released Friday show.

The county’s unemployment rate edged up for the second straight month from 5 percent in September and a low of 4.9 percent in August, according to figures from the California Employment Development Department. A year ago, the rate was 6.1 percent.

The main reason for last month’s increase was a sign of strength for the local economy: 25,000 people entered the labor force looking for work, bringing the total labor force to nearly 5.15 million. What’s more, 14,000 more people found work than lost their jobs during the month.

L.A. County’s unemployment rate was lower than the 5.5 percent statewide figure for October, though it was higher than the national rate of 4.9 percent.

On the jobs front, L.A. entered record territory as the number of payroll jobs reported by employers surged by 39,000 to reach 4.4 million in October. The gains were broad-based, including private education (up 7,700), local government (up 7,300), healthcare/social assistance (up 6,900) and retail trade (up 6,500). The entertainment sector also did well, posting a gain of about 4,500 jobs.

Many of the job gains were seasonal, including in education and retail. Adjusting for these seasonal factors, the job gain was much smaller, at just under 4,000.

The job gains in entertainment have been particularly robust, with companies adding positions at an accelerated rate, said Brandi Britton, district president for the Los Angeles region for Robert Half International, a Menlo Park staffing firm.

“There’s a lot more production going on in Los Angeles now, in part due to those state tax credits,” Britton said. “Many entertainment companies now feel a lot more optimistic about their future in Los Angeles.”

Only two sectors reported significant job reductions last month: construction and manufacturing, which each shed about 1,000 jobs.

For the 12 months ending in October, the county added 71,000 payroll jobs for a gain of 1.6 percent. The largest gain was healthcare/social assistance, which added 22,000 jobs, followed by accommodation/food services, up 11,700 jobs.

Manufacturing shed 6,000 jobs over the past 12 months, by far the biggest loser as that sector continues in long-term decline.

Public policy and energy reporter Howard Fine can be reached at [email protected]. Follow him on Twitter @howardafine.