105393202121088 has 384 divisors, whose sum is σ = 365067509664000. Its totient is φ = 28510321545216.

The previous prime is 105393202121083. The next prime is 105393202121153. The reversal of 105393202121088 is 880121202393501.

105393202121088 is a `hidden beast` number, since 1 + 0 + 5 + 3 + 9 + 320 + 212 + 108 + 8 = 666.

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

It is a super-2 number, since 2×105393202121088² (a number of 29 digits) contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105393202121083) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 255511431 + ... + 255923577.

It is an arithmetic number, because the mean of its divisors is an integer number (950696639750).

Almost surely, 2^{105393202121088} is an apocalyptic number.

105393202121088 is a gapful number since it is divisible by the number (18) 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 105393202121088, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (182533754832000).

105393202121088 is an abundant number, since it is smaller than the sum of its proper divisors (259674307542912).

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

105393202121088 is a wasteful number, since it uses less digits than its factorization.

105393202121088 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 413862 (or 413847 counting only the distinct ones).

The product of its (nonzero) digits is 207360, while the sum is 45.

The spelling of 105393202121088 in words is "one hundred five trillion, three hundred ninety-three billion, two hundred two million, one hundred twenty-one thousand, eighty-eight".