* Oct. jobless rate hits 13.5 percent, highest on record
* Number of unemployed jumps to 684,047, up 39 percent y/y
* Youth unemployment at 35 percent
(Adds details, analyst comment)
ATHENS, Jan 13 (Reuters) - Greece's unemployment rate hit a new record in October as an austerity programme designed to slash the budget deficit led to more job cuts, impacting more than a third of the workforce aged 24 and under, data showed.
The unemployment rate jumped to 13.5 percent from 12.6 percent in September and 9.8 percent in October 2009, Thursday's figures from statistics service ELSTAT showed, marking its highest reading since Greece started compiling monthly jobless data in 2004.
A record 684,047 people were officially without work, a 39 percent increase year-on-year.
"The end of the tourism season worsened conditions in the labour market, which remains extremely vulnerable in basic sectors of the economy such as construction," said Nikos Magginas, an economist at National Bank.
Employment is suffering as the Greek economy goes through its deepest recession in almost 40 years, hurt by austerity measures to shore up the country's finances and meet the terms of a 110 billion euro EU/IMF bailout.
Greece's jobless rate was the fourth-highest in the 16-member euro zone in October after Spain, Slovakia and Ireland, and 3.4 percentage points higher than the bloc's average.
The government expects unemployment to average out at 14.6 percent this year, as the economy goes through its third consecutive year of recession.
Unemployment stung young people hardest, with the jobless rate reaching 35 percent in the 15-24 age group and 18 percent for those aged 25 to 34.
(Additional reporting by Renee Maltezou)
(Reporting by Harry Papachristou; Editing by John Stonestreet)