349978728960 has 720 divisors, whose sum is σ = 1444544933832. Its totient is φ = 78033715200.

The previous prime is 349978728949. The next prime is 349978728961. The reversal of 349978728960 is 69827879943.

349978728960 is a `hidden beast` number, since 3 + 499 + 7 + 8 + 72 + 8 + 9 + 60 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 140859097344 + 209119631616 = 375312^2 + 457296^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×349978728960² (a number of 24 digits) contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (349978728961) by changing a digit.

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 71 ways as a sum of consecutive naturals, for example, 46283580 + ... + 46291140.

Almost surely, 2^349978728960 is an apocalyptic number.

349978728960 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 349978728960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (722272466916).

349978728960 is an abundant number, since it is smaller than the sum of its proper divisors (1094566204872).

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

349978728960 is a wasteful number, since it uses less digits than its factorization.

349978728960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7645 (or 7619 counting only the distinct ones).

The product of its (nonzero) digits is 329204736, while the sum is 72.

The spelling of 349978728960 in words is "three hundred forty-nine billion, nine hundred seventy-eight million, seven hundred twenty-eight thousand, nine hundred sixty".