19500

19500 is a natural number that sits between 19499 and 19501. In mathematics, it is an even, composite integer with several notable factorization properties.

Its prime factorization is 2^2 × 3 × 5^3 × 13. From this factorization, 19500 has 48 positive divisors. The number is divisible by 100 (and thus by 4 and 25), and it is also divisible by 3 and by 13; indeed 19500/3 = 6500, 19500/13 = 1500, and 19500/39 = 500. The digit sum is 1+9+5+0+0 = 15, which makes 19500 a Harshad (Niven) number in base 10, since 19500 ÷ 15 = 1300. It is also divisible by 500 (19500/500 = 39).

In common use, 19500 is a round-number figure often encountered in currency, statistics, and measurements, especially when written with thousand separators as 19,500. The number’s large number of divisors and its factor structure can be relevant in teaching contexts for illustrating divisor counts, factorization, and divisibility rules.

Beyond basic arithmetic, 19500 does not have widely recognized mathematical constants or theorems specifically associated with it. It serves mainly as an example of a highly composite, even integer with multiple small prime factors.