4008 has 16 divisors (see below), whose sum is σ = 10080. Its totient is φ = 1328.

The previous prime is 4007. The next prime is 4013. The reversal of 4008 is 8004.

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

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 4, base 8, base 9 and base 16.

It is a junction number, because it is equal to n+sod(n) for n = 3984 and 4002.

It is not an unprimeable number, because it can be changed into a prime (4001) 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 3 ways as a sum of consecutive naturals, for example, 60 + ... + 107.

It is an arithmetic number, because the mean of its divisors is an integer number (630).

It is an amenable number.

4008 is an abundant number, since it is smaller than the sum of its proper divisors (6072).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5040).

4008 is a wasteful number, since it uses less digits than its factorization.

4008 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 176 (or 172 counting only the distinct ones).

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

The square root of 4008 is about 63.3087671654. The cubic root of 4008 is about 15.8845861461.

The spelling of 4008 in words is "four thousand, eight".