345916720800 has 1728 divisors, whose sum is σ = 1613326740480. Its totient is φ = 70409502720.

The previous prime is 345916720759. The next prime is 345916720811. The reversal of 345916720800 is 8027619543.

345916720800 is a `hidden beast` number, since 34 + 591 + 6 + 7 + 20 + 8 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 439538007 + ... + 439538793.

It is an arithmetic number, because the mean of its divisors is an integer number (933638160).

It is a 1-persistent number, because it is pandigital, but 2⋅345916720800 = 691833441600 is not.

Almost surely, 2^345916720800 is an apocalyptic number.

345916720800 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 345916720800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (806663370240).

345916720800 is an abundant number, since it is smaller than the sum of its proper divisors (1267410019680).

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

345916720800 is a wasteful number, since it uses less digits than its factorization.

345916720800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 865 (or 840 counting only the distinct ones).

The product of its (nonzero) digits is 362880, while the sum is 45.

The spelling of 345916720800 in words is "three hundred forty-five billion, nine hundred sixteen million, seven hundred twenty thousand, eight hundred".