SAN JOSE — Hewlett-Packard said Tuesday it will lay off up to 33,000 more employees as the storied Silicon Valley tech giant prepares to split in two.

The layoffs — which are only the latest big cuts under CEO Meg Whitman — represent more than 10 percent of HP’s 300,000 employees worldwide. Company executives told financial analysts in a San Jose meeting that employee cuts and other restructuring would save at least $2.7 billion annually.

Analysts predicted the cuts will be painful, and speculated that they may be a prelude to selling off part of the corporation. Whitman said in a statement the cost cutting “will eliminate the need for any future corporate restructuring.” The company declined to comment on specific details.

Palo Alto-based Hewlett-Packard last October announced it was splitting into two companies: Hewlett Packard Enterprise, focused on business hardware, software and services, and HP Inc., encompassing the personal computer and printer unit. Between 25,000 and 30,000 cuts will come from Hewlett Packard Enterprise and an additional 3,300 from HP Inc.

Since 2012, the company has steadily announced a series of layoffs, totaling 55,000 jobs by 2014 as HP has struggled to respond to the consumer shift to smartphones and tablets from PCs and printers.

Hewlett Packard Enterprise will be “smaller and more focused” after the restructuring, Whitman said. “These restructuring activities will enable a more competitive, sustainable cost structure for the new Hewlett Packard Enterprise.” The company said it will also hire as it reshapes its workforce.

Oregon-based analyst Rob Enderle said Whitman tends to announce pending layoffs months before she cuts down the workforce. “She really drags them on, which is one of the reasons it has been so hard for HP to recover,” he said. “There’s hard feelings. It just creates this toxic environment.”

He said “you have to wonder how they’re going to get business done” with so many cuts, especially since the split of a company into two separate segments usually requires more workers, not fewer. The split is effective Nov. 1.

Enderle said one possibility is that Whitman is reducing costs to position the enterprise division for a sale to a big buyer such as Oracle. Larry Ellison, the longtime CEO and now chairman of Oracle, was never interested in HP’s computers and printers, but he could be interested in the enterprise division that sells servers, storage hardware and networking services, Enderle said.

“(He wants to) either buy them or take them out of business,” the analyst said. “This is a good day for Larry Ellison, not a good day for HP employees.”

Tech analyst Roger Kay, president of Massachusetts-based Endpoint Technologies Associates, said it was unclear where the company would cut. HP has offices in dozens of countries, including U.S. branches in Texas and Florida and Northern California offices in Palo Alto, Sunnyvale and Roseville. “There’s going to be a lot of concentric waves of pain that come out from this one,” he said.

The layoffs have political reverberations as well, as former HP CEO Carly Fiorina prepares to make her debut in Wednesday’s prime-time Republican presidential debate.

Fiorina became HP’s top executive in 1999 and now touts her record as the first woman to lead a Fortune 50 company as a key part of her qualifications to be the first woman in the Oval Office. Yet she presided over the layoffs of 30,000 HP employees, and she was fired by the board of directors in 2005 as the company’s stock plummeted. Unlike those she had laid off, however, she went out the door with a “golden parachute” of $21 million cash plus $19 million in stock and pension benefits.

Whitman — who ran unsuccessfully for governor in 2010, the same year that Fiorina ran unsuccessfully for U.S. Senate — has enacted many more layoffs at HP than Fiorina ever did. Still, the specter of more HP heads rolling can’t help Fiorina as she tries to build momentum.

“It will serve for some as a reminder of her tenure at HP, but I think the questions to Fiorina will go well beyond the 30,000 she laid off,” said Larry Gerston, a San Jose State political science professor emeritus.

HP had worldwide sales of $110 billion and ranked No. 2 in this year’s SV150, this newspaper’s ranking of the largest companies in Silicon Valley by revenue. HP has about 2,500 employees in Palo Alto and about 2,000 in Sunnyvale, according to economic development data from those cities.

State reports say the company has cut about 500 jobs in California since early 2014. The California Employment Development Department has not yet received any formal warnings from HP of major layoffs in Silicon Valley, meaning they cannot happen in the next 60 days. The last time HP notified the state was in July, when it cut 65 workers.

The company expects to find a total of $2.7 billion in annual savings at Hewlett Packard Enterprises. About $700 million would come from reorganization and adjustments to real estate strategy, the company said, while layoffs will save another $2 billion annually.

Hewlett Packard Enterprise expects to be strong in the areas of servers, storage and networking. The company also told analysts that it expects to invest heavily in cloud storage technology. HP expects cloud storage business to grow more than 20 percent for the next several years.

Staff writer Josh Richman contributed to this report. Contact Louis Hansen 408-920-5043. Follow him at Twitter.com/HansenLouis. Contact Matt O’Brien at 408-920-5011. Follow him at Twitter.com/Mattoyeah.