19800 has 72 divisors (see below), whose sum is σ = 72540. Its totient is φ = 4800.

The previous prime is 19793. The next prime is 19801. The reversal of 19800 is 891.

19800 = T₂₄ + T₂₅ + ... + T₅₀.

It is a tau number, because it is divible by the number of its divisors (72).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (19801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1795 + ... + 1805.

2¹⁹⁸⁰⁰ is an apocalyptic number.

19800 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 19800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (36270).

19800 is an abundant number, since it is smaller than the sum of its proper divisors (52740).

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

19800 is a wasteful number, since it uses less digits than its factorization.

19800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 33 (or 21 counting only the distinct ones).

The product of its (nonzero) digits is 72, while the sum is 18.

The square root of 19800 is about 140.7124727947. The cubic root of 19800 is about 27.0533922900.

It can be divided in two parts, 1 and 9800, that added together give a square (9801 = 99²).

The spelling of 19800 in words is "nineteen thousand, eight hundred".