5688

5688 is a natural number that comes after 5687 and before 5689. In mathematics, it is an even composite number with prime factorization 2^3 3^2 79.

It factors as 2^3 3^2 79 and can be expressed as 72 79. The number is divisible by 8, 9, 72, and 79.

5688 has 24 divisors. The sum of all divisors is 15600, so the sum of proper divisors is 9912. Because the sum of its proper divisors exceeds the number itself, 5688 is an abundant number.

In number theory, 5688 is also classified as a practical number, a positive integer for which every smaller positive integer can be represented as a sum of distinct divisors of the number. Its prime factorization 2^3 3^2 79 satisfies the practical-number criterion: after including 2^3 and 3^2, the next prime 79 is at most 1 plus the sum of divisors of the previous part.

There is no widely noted historical event or cultural significance associated with 5688; it is primarily treated as a numerical object in mathematics. See also: natural numbers, divisor function, abundant numbers, practical numbers.