105989309414208 has 2240 divisors, whose sum is σ = 377424487858176. Its totient is φ = 29084977152000.

The previous prime is 105989309414201. The next prime is 105989309414239. The reversal of 105989309414208 is 802414903989501.

105989309414208 is a `hidden beast` number, since 1 + 0 + 5 + 9 + 8 + 9 + 3 + 0 + 9 + 414 + 208 = 666.

It is a super-2 number, since 2×105989309414208² (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 (105989309414201) by changing a digit.

It is a polite number, since it can be written in 319 ways as a sum of consecutive naturals, for example, 266975590266 + ... + 266975590662.

Almost surely, 2^{105989309414208} is an apocalyptic number.

105989309414208 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 105989309414208, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (188712243929088).

105989309414208 is an abundant number, since it is smaller than the sum of its proper divisors (271435178443968).

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

105989309414208 is a wasteful number, since it uses less digits than its factorization.

105989309414208 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 634 (or 615 counting only the distinct ones).

The product of its (nonzero) digits is 22394880, while the sum is 63.

The spelling of 105989309414208 in words is "one hundred five trillion, nine hundred eighty-nine billion, three hundred nine million, four hundred fourteen thousand, two hundred eight".