It’s obvious that there’s 1760 yards in a mile.

There’s 22 yards in a chain, which we can all remember because of the 22 yard line in rugby.

There are 10 chains in a furlong, which fans of metric can’t complain about.

There are 8 furlongs in a mile, just like there are 8 pints in a gallon.

And 22x10x8 = 11x10x16 and 11 is easy to multiply by in your head, so it’s really very simple to get to 1760.

/s