105398506313856 has 384 divisors, whose sum is σ = 358634992435200. Its totient is φ = 29074798540800.

The previous prime is 105398506313839. The next prime is 105398506313869. The reversal of 105398506313856 is 658313605893501.

105398506313856 is a `hidden beast` number, since 1 + 0 + 5 + 3 + 98 + 506 + 3 + 1 + 38 + 5 + 6 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-2 number, since 2×105398506313856² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a junction number, because it is equal to n+sod(n) for n = 105398506313793 and 105398506313802.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 107253985 + ... + 108232223.

It is an arithmetic number, because the mean of its divisors is an integer number (933945292800).

Almost surely, 2^{105398506313856} is an apocalyptic number.

105398506313856 is a gapful number since it is divisible by the number (16) 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 105398506313856, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (179317496217600).

105398506313856 is an abundant number, since it is smaller than the sum of its proper divisors (253236486121344).

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

105398506313856 is a wasteful number, since it uses less digits than its factorization.

105398506313856 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 978728 (or 978713 counting only the distinct ones).

The product of its (nonzero) digits is 69984000, while the sum is 63.

The spelling of 105398506313856 in words is "one hundred five trillion, three hundred ninety-eight billion, five hundred six million, three hundred thirteen thousand, eight hundred fifty-six".