345385684800 has 840 divisors, whose sum is σ = 1414553863800. Its totient is φ = 82074746880.

The previous prime is 345385684757. The next prime is 345385684849. The reversal of 345385684800 is 8486583543.

345385684800 is a `hidden beast` number, since 3 + 4 + 5 + 38 + 568 + 48 + 0 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 175654868544 + 169730816256 = 419112^2 + 411984^2 .

It is a Harshad number since it is a multiple of its sum of digits (54).

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 119 ways as a sum of consecutive naturals, for example, 48855666 + ... + 48862734.

It is an arithmetic number, because the mean of its divisors is an integer number (1683992695).

Almost surely, 2^345385684800 is an apocalyptic number.

345385684800 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 345385684800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (707276931900).

345385684800 is an abundant number, since it is smaller than the sum of its proper divisors (1069168179000).

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

345385684800 is a wasteful number, since it uses less digits than its factorization.

345385684800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7145 (or 7121 counting only the distinct ones).

The product of its (nonzero) digits is 11059200, while the sum is 54.

The spelling of 345385684800 in words is "three hundred forty-five billion, three hundred eighty-five million, six hundred eighty-four thousand, eight hundred".