105828508800 has 1920 divisors, whose sum is σ = 489240829440. Its totient is φ = 21976842240.

The previous prime is 105828508789. The next prime is 105828508829. The reversal of 105828508800 is 8805828501.

105828508800 is a `hidden beast` number, since 10 + 58 + 2 + 8 + 508 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1920).

It is a super-2 number, since 2×105828508800² (a number of 23 digits) contains 22 as substring.

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

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 239 ways as a sum of consecutive naturals, for example, 1449705564 + ... + 1449705636.

It is an arithmetic number, because the mean of its divisors is an integer number (254812932).

Almost surely, 2^105828508800 is an apocalyptic number.

105828508800 is a gapful number since it is divisible by the number (10) 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 105828508800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (244620414720).

105828508800 is an abundant number, since it is smaller than the sum of its proper divisors (383412320640).

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

105828508800 is a wasteful number, since it uses less digits than its factorization.

105828508800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 180 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 204800, while the sum is 45.

The spelling of 105828508800 in words is "one hundred five billion, eight hundred twenty-eight million, five hundred eight thousand, eight hundred".