7872 has 28 divisors (see below), whose sum is σ = 21336. Its totient is φ = 2560.

The previous prime is 7867. The next prime is 7873. The reversal of 7872 is 2787.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an alternating number because its digits alternate between odd and even.

Its product of digits (784) is a multiple of the sum of its prime factors (56).

It is a plaindrome in base 13.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 7872.

It is not an unprimeable number, because it can be changed into a prime (7873) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 172 + ... + 212.

It is an arithmetic number, because the mean of its divisors is an integer number (762).

2⁷⁸⁷² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10668).

7872 is an abundant number, since it is smaller than the sum of its proper divisors (13464).

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

7872 is a wasteful number, since it uses less digits than its factorization.

7872 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 56 (or 46 counting only the distinct ones).

The product of its digits is 784, while the sum is 24.

The square root of 7872 is about 88.7242920513. The cubic root of 7872 is about 19.8927593331.

The spelling of 7872 in words is "seven thousand, eight hundred seventy-two".