5840

5840 is a natural number following 5839 and preceding 5841. It is an even composite number with a prime factorization of 2^4 × 5 × 73, which reveals its divisibility properties and internal structure.

The prime factorization shows the number has 20 positive divisors (computed from the exponents 4, 1, and 1 as (4+1)×(1+1)×(1+1)). Notable divisors include 2, 4, 5, 8, 10, 16, 20, 40, 73, 146, 365, 730, 1460, 2920, and 5840, among others. In addition, 5840 can be expressed as 73 × 80.

Key arithmetic properties include the sum of divisors, sigma(5840) = 13,764, and Euler’s totient function, φ(5840) = 2,304. The sum of proper divisors is 13,764 − 5,840 = 7,924, which is greater than 5,840, making 5840 an abundant number. Its abundancy categorizes it among even abundant numbers, a class of integers with a proper divisor sum exceeding the number itself.

In other bases, 5840 is 0x16D0 in hexadecimal and 0b1011011010000 in binary. It can also be factored as 73 × 80, highlighting its decomposition into a large prime factor and a power-of-two-times-five component.

Overall, 5840 is notable primarily for its factorization and arithmetic characteristics within number theory, rather than for any widely cited cultural or historical significance.