1034

1034, written as one thousand thirty-four, is a natural number that follows 1033 and precedes 1035. It is an even, composite, square-free integer with prime factorization 2 × 11 × 47.

Its positive divisors are 1, 2, 11, 22, 47, 94, 517, and 1034, giving a total of eight divisors. Because it is the product of three distinct primes, 1034 is square-free and not a prime power.

In arithmetic, Euler’s totient function yields φ(1034) = 460, and the sum of its divisors is σ(1034) = 1728, which equals 12 cubed. These values reflect its factorization and divisor structure.

In numeral systems, 1034 is represented as binary 10000001010, hexadecimal 0x40A, and octal 2012. In Roman numerals, it is written as MXXXIV (1000 + 30 + 4).

As a calendar year, 1034 CE falls in the 11th century of the early medieval period. Historical notes for that year depend on regional sources and are not part of a single unified event list.

Overall, 1034 is a modestly composite integer with distinct prime factors, notable for its simple divisor structure and straightforward representations across several common bases.