The crisp new dollar bill that I have just taken from my wallet bears the serial number 24598176. It’s easy to tell that the number is exactly divisible by 2 but not by 5. Is it divisible by 3? by 4? by 11?
In a 1962 Scientific American article, Martin Gardner noted that during the 15th and 16th centuries in Renaissance Europe, the rules for checking whether one number is divisible by another without a remainder were widely known, particularly because of their usefulness in reducing large-number fractions to their lowest terms.