34800192000 has 1200 divisors, whose sum is σ = 151893624168. Its totient is φ = 7896268800.

The previous prime is 34800191981. The next prime is 34800192019. The reversal of 34800192000 is 29100843.

It is an interprime number because it is at equal distance from previous prime (34800191981) and next prime (34800192019).

It can be written as a sum of positive squares in 4 ways, for example, as 11632916736 + 23167275264 = 107856^2 + 152208^2 .

It is a tau number, because it is divible by the number of its divisors (1200).

It is a super-2 number, since 2×34800192000² (a number of 22 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 254015932 + ... + 254016068.

Almost surely, 2^34800192000 is an apocalyptic number.

34800192000 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 34800192000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (75946812084).

34800192000 is an abundant number, since it is smaller than the sum of its proper divisors (117093432168).

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

34800192000 is an equidigital number, since it uses as much as digits as its factorization.

34800192000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 196 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

Adding to 34800192000 its reverse (29100843), we get a palindrome (34829292843).

The spelling of 34800192000 in words is "thirty-four billion, eight hundred million, one hundred ninety-two thousand".