349728768000 has 768 divisors, whose sum is σ = 1291836405600. Its totient is φ = 90990182400.

The previous prime is 349728767987. The next prime is 349728768017. The reversal of 349728768000 is 867827943.

349728768000 is a `hidden beast` number, since 3 + 497 + 2 + 8 + 76 + 80 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (768).

It is a super-2 number, since 2×349728768000² (a number of 24 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1953791911 + ... + 1953792089.

Almost surely, 2^349728768000 is an apocalyptic number.

349728768000 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 349728768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (645918202800).

349728768000 is an abundant number, since it is smaller than the sum of its proper divisors (942107637600).

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

349728768000 is an equidigital number, since it uses as much as digits as its factorization.

349728768000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 283 (or 242 counting only the distinct ones).

The product of its (nonzero) digits is 4064256, while the sum is 54.

The spelling of 349728768000 in words is "three hundred forty-nine billion, seven hundred twenty-eight million, seven hundred sixty-eight thousand".