* 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
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr
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 worse-than-expected euro zone inflation number pushed back prospects for monetary policy tightening well into the future.
Long-dated bonds are the most sensitive to any change in interest rates, so the disappointing consumer price figure from the bloc released the previous day boosted demand for 30-year euro zone government bonds.
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.
"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 move inversely to prices -- down 3-4 bps on the day.
France's 30-year yield, for example, was close to its lowest level in over a year at 151 basis points.
In the more conventional 10-year space, euro zone bond yields were lower 1-2 bps across the board.
These 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 likely also having an effect: the U.S. Treasury yield curve has been at its flattest levels in over 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.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s
(Reporting by Abhinav Ramnarayan; Editing by Richard Balmforth)