105984073728 has 896 divisors, whose sum is σ = 369915033600. Its totient is φ = 29727129600.

The previous prime is 105984073711. The next prime is 105984073729. The reversal of 105984073728 is 827370489501.

It is a happy number.

105984073728 is a `hidden beast` number, since 1 + 0 + 598 + 40 + 7 + 3 + 7 + 2 + 8 = 666.

It is a super-2 number, since 2×105984073728² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105984073729) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 2584977388 + ... + 2584977428.

It is an arithmetic number, because the mean of its divisors is an integer number (412851600).

Almost surely, 2^105984073728 is an apocalyptic number.

105984073728 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 105984073728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184957516800).

105984073728 is an abundant number, since it is smaller than the sum of its proper divisors (263930959872).

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

105984073728 is a wasteful number, since it uses less digits than its factorization.

105984073728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 149 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 3386880, while the sum is 54.

The spelling of 105984073728 in words is "one hundred five billion, nine hundred eighty-four million, seventy-three thousand, seven hundred twenty-eight".