One millibar is exactly one hectopascal. They are the same quantity with two names, which is unusual enough to be worth a page: the change from one to the other was a rename, not a conversion, and no weather chart ever had to be redrawn.
About the units
The millibar is a thousandth of a bar, and since the bar is exactly 100,000 pascals, a millibar is exactly 100 pascals. The hectopascal is a hundred pascals by definition of the prefix hecto. They are therefore identical. Meteorology adopted the millibar in the early twentieth century and switched to the hectopascal during the 1980s as national weather services moved to strict SI naming. Because the numbers were unchanged, the transition was invisible to the public — a low of 980 mbar simply became a low of 980 hPa, and older charts remain readable without any adjustment.
The exact factor
The factor is exactly 1. What this page is actually useful for is the neighbouring relationships. Standard sea level pressure is 1,013.25 hPa, which is one standard atmosphere and 1.01325 bar. Typical weather systems range from about 950 hPa in a deep depression to 1,050 hPa in a strong anticyclone. The lowest sea-level pressure ever recorded was 870 hPa in Typhoon Tip in 1979. In aviation, the altimeter setting QNH is given in hectopascals in most of the world and in inches of mercury in North America, where 1,013 hPa corresponds to 29.92 inHg.
Where you meet this conversion
Weather reporting, aviation and barometry. Surface pressure charts, forecasts and aircraft altimeter settings all use hectopascals outside North America, and older equipment and publications use millibars for the same values. Some marine barometers are still marked in millibars while the forecast they are compared against is issued in hectopascals — and the correct action is to read the number straight across without adjustment.