220

220 is a natural number that comes after 219 and before 221. In base-10 notation it consists of three digits: two hundred and twenty. It is an even number, being divisible by two, and is a composite number with many divisors.

In number theory, 220 is notable as the smaller member of the first known pair of amicable numbers (numbers of which each equals the sum of the other's proper divisors): 220 and 284. This pair is attested in early mathematical writings.

Mathematical properties

The prime factorization of 220 is 2² × 5 × 11. It has 12 positive divisors: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and 220. The sum of all its divisors is 504, while the sum of its proper divisors (those less than the number itself) is 284.

220 and 284

Two numbers are called amicable if the sum of the proper divisors of each equals the other. The proper divisors of 220 sum to 284, while those of 284 (1, 2, 4, 71, 142) sum to 220. Because of this relationship, these two numbers have been regarded as remarkable throughout the history of mathematics and science.

Other uses

In many parts of the world, 220 is used as the standard electrical voltage for households (measured in volts), though the official voltage varies from country to country. 220 also appears in sporting measurements (for example, a race of 220 yards, which was formerly used) and in other standardized figures.