Yes,
Early man-made computers (called the “computer” because mathematical calculations were originally performed by women who used to be called, in French, “Les ordinateurs”) could perform 20-plus digit multiplication. They were never hooked up physically though, and instead, people would whisper numbers to one another for hours or days until they are managed to get the number close enough that their whispers would merit a calculation.
Betcha don’t know what they call someone who did this? That’s right – an ungodly long long time ago… They called them calculators.