10004034440400 has 3840 divisors, whose sum is σ = 46815435620352. Its totient is φ = 1759739904000.

The previous prime is 10004034440399. The next prime is 10004034440423. The reversal of 10004034440400 is 404443040001.

10004034440400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 767 ways as a sum of consecutive naturals, for example, 73022149132 + ... + 73022149268.

Almost surely, 2^{10004034440400} is an apocalyptic number.

10004034440400 is a gapful number since it is divisible by the number (10) 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 10004034440400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (23407717810176).

10004034440400 is an abundant number, since it is smaller than the sum of its proper divisors (36811401179952).

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

10004034440400 is a wasteful number, since it uses less digits than its factorization.

10004034440400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 310 (or 299 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 24.

Adding to 10004034440400 its reverse (404443040001), we get a palindrome (10408477480401).

The spelling of 10004034440400 in words is "ten trillion, four billion, thirty-four million, four hundred forty thousand, four hundred".