105857388648000 has 3584 divisors, whose sum is σ = 456784356188160. Its totient is φ = 23758479360000.

The previous prime is 105857388647971. The next prime is 105857388648017. The reversal of 105857388648000 is 846883758501.

105857388648000 is a `hidden beast` number, since 1 + 0 + 5 + 8 + 5 + 73 + 8 + 86 + 480 + 0 + 0 = 666.

It is a super-2 number, since 2×105857388648000² (a number of 29 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 511 ways as a sum of consecutive naturals, for example, 154988855659 + ... + 154988856341.

It is an arithmetic number, because the mean of its divisors is an integer number (127450992240).

Almost surely, 2^{105857388648000} is an apocalyptic number.

105857388648000 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 105857388648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (228392178094080).

105857388648000 is an abundant number, since it is smaller than the sum of its proper divisors (350926967540160).

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

105857388648000 is a wasteful number, since it uses less digits than its factorization.

105857388648000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 851 (or 825 counting only the distinct ones).

The product of its (nonzero) digits is 51609600, while the sum is 63.

The spelling of 105857388648000 in words is "one hundred five trillion, eight hundred fifty-seven billion, three hundred eighty-eight million, six hundred forty-eight thousand".