* Euro zone 30-year bonds outperform, yields lower 3-4 bps
* Low inflation pushes back ECB tightening expectations
* Euro zone factories have busiest month for 17 years-PMIs
* Mystery move in EONIA rates baffles market participants
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Adds background, updates prices)
LONDON, Dec 1 (Reuters) - The gap between German 10-year and 30-year borrowing costs was at its tightest level since late August on Friday as a lower-than-expected euro zone inflation number pushed back prospects for monetary policy tightening well into the future.
Most euro zone government bond yields dropped on Friday, falling around 3-4 basis points across the board, a move that was attributed both to low inflation and to a delay in the U.S. Senate voting on a Republican tax overhaul.
Euro zone inflation rose by less than expected in November, highlighting that price growth remains weak in the bloc and supporting the European Central Bank's plan to remove stimulus only gradually.
Long-dated bonds are the most sensitive to any change in interest rates, so the consumer price figure released the previous day boosted demand for 30-year euro zone government bonds.
"People were like wow, this pushes back rate normalisation and also creates expectations that the ECB won't end QE too soon, so the rally in (long-dated) Bunds makes complete sense," said ING strategist Martin van Vliet.
The gap between German 10-year and 30-year borrowing costs went as low as 75 basis points, its tightest since August 24, according to Tradeweb prices.
Other 30-year euro zone government bonds were also in demand, with yields -- which fall as prices rise -- down 5-6 bps on the day.
France's 30-year yield, for example, was close to its lowest level in more than a year at 1.49 percent.
Some also attributed the fall in euro zone bond yields to the delay in voting on U.S. tax reforms.
"A delay feeds into the notion that we are seeing an Obamacare part 2, that is, another key policy promise of Trumps collapsing," said Rabobank strategist Richard McGuire, referring to U.S. President Donald Trump's unsuccessful attempt to repeal the health care act brought in by his predecessor Barack Obama.
"Tax reforms would be positive for growth and inflation and therefore bearish for safe haven U.S. Treasuries and Bunds," said McGuire.
The yield curve spreads have also been pushed tighter by increased buying by insurance companies, who typically buy long-dated assets to match their liabilities, and often do their buying towards the end of the year, said van Vliet.
The trend in United States government debt is probably also having an effect: the U.S. Treasury yield curve has been at its flattest levels in more than a decade, raising concerns over when the expansion in the world's biggest economy will come to an end.
Many investors switch between the debt of the world's developed economies, so the yields of Japanese, European and U.S. debt tend to move in sympathy with each other.
Signs of economic strength continued to hit the screens.
Euro zone factories had their busiest month for over 17 years in November in a broad based acceleration, a purchasing managers' index showed, despite them hiking prices at the fastest rate in more than six years.
Investors were also left baffled by a sharp, unexplained move this week in a key European money market rate.
The Euro Over Night Index Average (EONIA) has spiked 8 basis points since the start of the week to its highest since mid-March at minus 24 basis points, Reuters data showed.
Rabobank analysts said there has been "no convincing explanation" for the move, but said it may have been caused by one bank in need of funds against a backdrop of an illiquid market.
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(Reporting by Abhinav Ramnarayan; Editing by Richard Balmforth and Peter Graff)