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?

We represent a number by a sequence of digits. For example, 532 represents a number made up of five 100s, three 10s and two units. Three 10s (30) is divisible by two, because 10 is. Similarly, 500 is ...