2004416300400 has 480 divisors, whose sum is σ = 7200090736128. Its totient is φ = 474007142400.

The previous prime is 2004416300389. The next prime is 2004416300431. The reversal of 2004416300400 is 40036144002.

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 pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 31404520 + ... + 31468280.

Almost surely, 2^{2004416300400} is an apocalyptic number.

2004416300400 is a gapful number since it is divisible by the number (20) 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 2004416300400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (3600045368064).

2004416300400 is an abundant number, since it is smaller than the sum of its proper divisors (5195674435728).

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

2004416300400 is a wasteful number, since it uses less digits than its factorization.

2004416300400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 63889 (or 63878 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 24.

The spelling of 2004416300400 in words is "two trillion, four billion, four hundred sixteen million, three hundred thousand, four hundred".