4008004000000 has 1701 divisors, whose sum is σ = 13845956617143. Its totient is φ = 1153152000000.

The previous prime is 4008003999983. The next prime is 4008004000019. The reversal of 4008004000000 is 4008004.

The square root of 4008004000000 is 2002000.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 10 ways, for example, as 1880233318656 + 2127770681344 = 1371216^2 + 1458688^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is an unprimeable number.

It is a polite number, since it can be written in 188 ways as a sum of consecutive naturals, for example, 308307999994 + ... + 308308000006.

Almost surely, 2^{4008004000000} is an apocalyptic number.

4008004000000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

4008004000000 is the 2002000-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4008004000000

4008004000000 is an abundant number, since it is smaller than the sum of its proper divisors (9837952617143).

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

4008004000000 is an frugal number, since it uses more digits than its factorization.

4008004000000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 108 (or 38 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 16.

Multiplying 4008004000000 by its sum of digits (16), we get a square (64128064000000 = 8008000²).

4008004000000 divided by its sum of digits (16) gives a square (250500250000 = 500500²).

Adding to 4008004000000 its reverse (4008004), we get a palindrome (4008008008004).

4008004000000 divided by its reverse (4008004) gives a 6-th power (1000000 = 10⁶).

The spelling of 4008004000000 in words is "four trillion, eight billion, four million", and thus it is an aban number.