One inch is one twelfth of a foot, so 12 inches make a foot exactly. The twelve is not an accident of history to be apologised for — it was chosen because twelve divides evenly by two, three, four and six, which matters enormously when you are working without a calculator.
About the units
The foot and the inch are the two units of the imperial system that people actually handle. Both are defined from the yard: a foot is a third of a yard, exactly 0.3048 m, and an inch is a thirty-sixth of a yard, exactly 25.4 mm. The inch's name comes from the Latin uncia, meaning a twelfth part — the same root that gives us the ounce, which was originally a twelfth of a Roman pound. That shared origin is the clue to the whole system: duodecimal subdivision was standard across Roman and medieval European measurement because it makes thirds and quarters exact where decimal makes them repeating.
The exact factor
The factor is exactly 12, and both directions are exact. Where it gets interesting is in the mixed notation the pair is normally written in. A height of 70 inches is 5 feet 10 inches, found by dividing by 12 to get whole feet and keeping the remainder as inches. Decimal feet exist in surveying — 5.83 feet — but almost nowhere else, and mixing the two conventions is a real source of error: 5.10 feet is not five feet ten inches, it is five feet and about one and a quarter inches.
Where you meet this conversion
Heights of people, doors, ceilings and vehicles are the everyday case in the United States, the United Kingdom and much of the Commonwealth. Construction lumber is sold in feet with cross-sections in inches, so a two-by-four eight feet long is 1.5 by 3.5 inches by 96 inches — and the nominal dimensions do not match the actual ones, which is a separate trap. Shoe sizes, tyre diameters and television screens all use inches while the objects around them are measured in feet.