105882381688320 has 640 divisors, whose sum is σ = 377136963118080. Its totient is φ = 28157815848960.

The previous prime is 105882381688301. The next prime is 105882381688333. The reversal of 105882381688320 is 23886183288501.

It is a happy number.

105882381688320 is a `hidden beast` number, since 1 + 0 + 588 + 2 + 3 + 8 + 16 + 8 + 8 + 32 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (640).

It is a super-3 number, since 3×105882381688320³ (a number of 43 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 66300801762 + ... + 66300803358.

It is an arithmetic number, because the mean of its divisors is an integer number (589276504872).

Almost surely, 2^{105882381688320} is an apocalyptic number.

105882381688320 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 105882381688320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (188568481559040).

105882381688320 is an abundant number, since it is smaller than the sum of its proper divisors (271254581429760).

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

105882381688320 is a wasteful number, since it uses less digits than its factorization.

105882381688320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3663 (or 3641 counting only the distinct ones).

The product of its (nonzero) digits is 35389440, while the sum is 63.

The spelling of 105882381688320 in words is "one hundred five trillion, eight hundred eighty-two billion, three hundred eighty-one million, six hundred eighty-eight thousand, three hundred twenty".