8004 has 24 divisors (see below), whose sum is σ = 20160. Its totient is φ = 2464.

The previous prime is 7993. The next prime is 8009. The reversal of 8004 is 4008.

8004 is nontrivially palindromic in base 7.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a plaindrome in base 15.

It is not an unprimeable number, because it can be changed into a prime (8009) by changing a digit.

8004 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 7 ways as a sum of consecutive naturals, for example, 262 + ... + 290.

It is an arithmetic number, because the mean of its divisors is an integer number (840).

2⁸⁰⁰⁴ 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 8004, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10080).

8004 is an abundant number, since it is smaller than the sum of its proper divisors (12156).

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

8004 is a wasteful number, since it uses less digits than its factorization.

8004 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 59 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 32, while the sum is 12.

The square root of 8004 is about 89.4650769854. The cubic root of 8004 is about 20.0033327779.

The spelling of 8004 in words is "eight thousand, four".