105867878400 has 504 divisors, whose sum is σ = 399310067520. Its totient is φ = 26736721920.

The previous prime is 105867878387. The next prime is 105867878453. The reversal of 105867878400 is 4878768501.

It is a happy number.

105867878400 is a `hidden beast` number, since 10 + 586 + 7 + 8 + 7 + 8 + 40 + 0 = 666.

It is a super-2 number, since 2×105867878400² (a number of 23 digits) contains 22 as substring.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 35019289 + ... + 35022311.

It is an arithmetic number, because the mean of its divisors is an integer number (792281880).

Almost surely, 2^105867878400 is an apocalyptic number.

105867878400 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 105867878400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (199655033760).

105867878400 is an abundant number, since it is smaller than the sum of its proper divisors (293442189120).

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

105867878400 is a wasteful number, since it uses less digits than its factorization.

105867878400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3084 (or 3052 counting only the distinct ones).

The product of its (nonzero) digits is 3010560, while the sum is 54.

The spelling of 105867878400 in words is "one hundred five billion, eight hundred sixty-seven million, eight hundred seventy-eight thousand, four hundred".