1578

1578 is an integer that lies between 1577 and 1579. It is an even and composite number with prime factorization 2 × 3 × 263, making it square-free and contributing eight positive divisors: 1, 2, 3, 6, 263, 526, 789, and 1578.

As a sum of divisors, the proper divisors total 1590, which means 1578 is an abundant number. It is also semiperfect, since 789 + 526 + 263 equals 1578, a property that indicates some subset of proper divisors sums to the number itself. The digit sum is 21, so 1578 is divisible by 3 but not by 9; it is also divisible by 2 and 3, but not by 5. The Euler totient function yields φ(1578) = 524.

In various base representations, 1578 appears as 11000101010 in binary, 0x62A in hexadecimal, and 0o3052 in octal. In Roman numerals, it is written as MDLXXVIII.

Recent interest in 1578 often centers on its mathematical properties rather than any widespread cultural references. As a member of the even, composite numbers, it participates in standard divisor-related concepts such as factorization, divisors, and semiperfect numbers. Its Factorization and representations illustrate common techniques used to analyze integers in number theory.