One week is exactly 7 days. Of all the units on this site, the week is the only one with no astronomical basis whatsoever — it does not divide the year, the month or anything else evenly, and it exists purely by cultural convention.
About the units
The seven-day week is usually traced to Babylonian astronomy, where seven celestial bodies were visible to the naked eye and moved against the fixed stars: the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. The names survive directly in the Romance languages and, through Norse equivalents, in English and the Nordic languages — Tuesday from Tiw for Mars, Wednesday from Woden for Mercury, Thursday from Thor for Jupiter. Attempts to change it have all failed: the French Republican calendar used ten-day décades from 1793, and the Soviet Union tried five- and six-day weeks between 1929 and 1940. Both were abandoned, in the Soviet case partly because a week that does not give everyone the same day off destroys family life.
The exact factor
The factor is exactly 7. What makes the week awkward is everything it does not divide into: a common year is 52 weeks and 1 day, a leap year 52 weeks and 2 days, which is why a given date shifts one weekday each year and two across a leap year. A month is never a whole number of weeks. The ISO 8601 week-numbering year handles this by defining weeks that always start on Monday and assigning each week to the year containing its Thursday, which means some years have 53 weeks and the first days of January can belong to the previous week-year.
Where you meet this conversion
Payroll, project scheduling, pregnancy dating and retail reporting. Gestational age is counted in weeks and days — "32 weeks and 4 days" is 228 days — because the resolution matters clinically. Business reporting often uses 4-4-5 accounting periods, which group weeks into months of 4, 4 and 5 weeks so that each quarter contains exactly 13 weeks, precisely because calendar months do not align with weeks. Sprint planning in software uses weeks throughout.