19500 has 48 divisors (see below), whose sum is σ = 61152. Its totient is φ = 4800.

The previous prime is 19489. The next prime is 19501. The reversal of 19500 is 591.

19500 = T₂₅ + T₂₆ + ... + T₅₀.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 5.

It is a zygodrome in base 5.

It is a self number, because there is not a number n which added to its sum of digits gives 19500.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 19500.

It is not an unprimeable number, because it can be changed into a prime (19501) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1494 + ... + 1506.

It is an arithmetic number, because the mean of its divisors is an integer number (1274).

2¹⁹⁵⁰⁰ is an apocalyptic number.

19500 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

19500 is the 75-th nonagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 19500, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (30576).

19500 is an abundant number, since it is smaller than the sum of its proper divisors (41652).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

19500 is a wasteful number, since it uses less digits than its factorization.

19500 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35 (or 23 counting only the distinct ones).

The product of its (nonzero) digits is 45, while the sum is 15.

The square root of 19500 is about 139.6424004377. The cubic root of 19500 is about 26.9160630604.

The spelling of 19500 in words is "nineteen thousand, five hundred".