Because there’s a hidden system of measurement change hiding in the middle. Inches, Feet and Yards are familiar 12:1 and 3:1 conversions, and Rods, Chains, Furlongs and Miles. Their conversation rates are generally nice conversion, with rations of 4 rods : 1 chain, 10 chains : 1 furlong, and 8 furlongs : 1 mile.

So where do we get 5,280 with prime factors of 2^5, 3, 5 and 11? Because a chain is 22 yards long. Why? Because somewhere along the line, inches, feet and yards went to a smaller standard, and the nice round 5 yards per rods became 5 and 1/2 yards per rod. Instead of a mile containing 4,800 feet (with quarters, twelfths and hundredths of miles all being nice round numbers of feet), it contained an extra 480 feet that were 1/11th smaller than the old feet.