19488

19488 is a natural number that follows 19487 and precedes 19489. It is an even, composite number with a prime factorization of 2^5 × 3 × 7 × 29, which makes it divisible by 2, 3, 7 and 29, as well as by powers of two up to 32.

As a product of four prime factors (with one repeated factor 2^5), 19488 has 48 positive divisors. The sum of its divisors, including the number itself, is 60,480, so the sum of its proper divisors is 40,992. Since this sum exceeds the number itself, 19488 is classified as an abundant number. Its abundance (the excess over the number) is 21,504.

In various numeral systems, 19488 can be expressed as:

- Binary: 1001100001000002

- Hexadecimal: 0x4C20

- Octal: 46040

These representations reflect its factorization and divisibility properties. In mathematical contexts, 19488 often appears as an example of a relatively large, highly composite-like number with multiple small prime factors, useful for illustrating divisor functions, factorization, and abundance calculations. Its neighbors, 19487 and 19489, are not divisible by the same small factors, highlighting how small changes in value can alter divisibility profiles.

See also: numbers surrounding 19488, such as 19487 and 19489, and general references on divisor functions and abundant numbers.