2005006218400 has 288 divisors, whose sum is σ = 5042567380032. Its totient is φ = 778191667200.

The previous prime is 2005006218367. The next prime is 2005006218409. The reversal of 2005006218400 is 48126005002.

It is not an unprimeable number, because it can be changed into a prime (2005006218409) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2210590747 + ... + 2210591653.

It is an arithmetic number, because the mean of its divisors is an integer number (17508914514).

Almost surely, 2^{2005006218400} is an apocalyptic number.

2005006218400 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 2005006218400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2521283690016).

2005006218400 is an abundant number, since it is smaller than the sum of its proper divisors (3037561161632).

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

2005006218400 is a wasteful number, since it uses less digits than its factorization.

2005006218400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1552 (or 1539 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 28.

The spelling of 2005006218400 in words is "two trillion, five billion, six million, two hundred eighteen thousand, four hundred".