19872 has 48 divisors (see below), whose sum is σ = 60480. Its totient is φ = 6336.

The previous prime is 19867. The next prime is 19889. The reversal of 19872 is 27891.

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (27).

Its product of digits (1008) is a multiple of the sum of its prime divisors (28).

It is a nialpdrome in base 12.

It is a congruent number.

It is an unprimeable number.

19872 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 853 + ... + 875.

It is an arithmetic number, because the mean of its divisors is an integer number (1260).

2¹⁹⁸⁷² is an apocalyptic number.

19872 is a gapful number since it is divisible by the number (12) 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 19872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (30240).

19872 is an abundant number, since it is smaller than the sum of its proper divisors (40608).

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

19872 is a wasteful number, since it uses less digits than its factorization.

19872 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 28 counting only the distinct ones).

The product of its digits is 1008, while the sum is 27.

The square root of 19872 is about 140.9680814936. The cubic root of 19872 is about 27.0861446128.

The spelling of 19872 in words is "nineteen thousand, eight hundred seventy-two".