349468838409600 has 6912 divisors, whose sum is σ = 1715181721344000. Its totient is φ = 67105093386240.

The previous prime is 349468838409553. The next prime is 349468838409617. The reversal of 349468838409600 is 6904838864943.

349468838409600 is a `hidden beast` number, since 3 + 4 + 9 + 4 + 6 + 8 + 8 + 3 + 8 + 4 + 0 + 9 + 600 = 666.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 863 ways as a sum of consecutive naturals, for example, 4423656182361 + ... + 4423656182439.

Almost surely, 2^{349468838409600} is an apocalyptic number.

349468838409600 is a gapful number since it is divisible by the number (30) 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 349468838409600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (857590860672000).

349468838409600 is an abundant number, since it is smaller than the sum of its proper divisors (1365712882934400).

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

349468838409600 is a wasteful number, since it uses less digits than its factorization.

349468838409600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 213 (or 165 counting only the distinct ones).

The product of its (nonzero) digits is 859963392, while the sum is 72.

The spelling of 349468838409600 in words is "three hundred forty-nine trillion, four hundred sixty-eight billion, eight hundred thirty-eight million, four hundred nine thousand, six hundred".