450

450 is a natural number that follows 449 and precedes 451. In mathematics, it is an even, composite number with a notable prime factorization.

The prime factorization of 450 is 2 × 3^2 × 5^2. From this factorization, it has 18 positive divisors. The sum of all divisors is 1209, so the sum of proper divisors is 759. Because 759 > 450, 450 is an abundant number. The Euler totient of 450 is φ(450) = 120, indicating the number of integers up to 450 that are relatively prime to 450.

450 is also a practical number, meaning that every smaller positive integer can be expressed as a sum of distinct divisors of 450. This property follows from its prime factorization and the standard practical-number criterion.

In various bases, 450 has the representations: decimal 450, binary 111000010, octal 702, and hexadecimal 0x1C2. In Roman numerals, 450 is written as CDL.

As a calendar year, 450 CE sits in late antiquity, a period marked by the later stages of the Western Roman Empire and various cross-cultural interactions. Notably, this era encompasses the activities of groups such as the Huns in Europe, with large-scale campaigns occurring in the subsequent years.

Summary: 450 is an even, abundant, composite number with diverse mathematical properties (factorization 2 × 3^2 × 5^2; 18 divisors; φ(450) = 120), practical-number status, and several standard representations across numeral systems, as well as cultural context as a calendar year.