Zero has no value when it stands by itself. When a zero is placed to the right of a number, it increases the value N-fold (where N, say 10, is the Base or Radix of the Number System.
Ten stands for the number of fingers on our hands. It is used as the Base of the Decimal Number System. 10/10 (Ten out of Ten) is a perfect score in some contests (e.g. gymnastics, diving).
Twenty is known as a “Score”. Abraham Lincoln’s famous Gettysburg Address starts with “Four scores and seven years ago”. In French and Pali, the number 80 is expressed as four 20s (instead of eight tens). A card name is known as Vingt-e-un (Twenty One).
Per Dr. Kyaw Tint] : Maybe because we have 10 fingers and 10 toes, altogether adding up to score.
Sixty has many factors : 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 …
It is used as a Base for Time and Angles.
e.g 1 minute = 60 seconds
1 hour = 60 minutes
Powers of 2
Two is used as a Base for the Binary Number System.
Digital computers extensively use the system.
Four, Eight and Sixteen are used as Bases (in Computer Science).