106929083785104 has 405 divisors, whose sum is σ = 350201434400337. Its totient is φ = 30368757694464.

The previous prime is 106929083785093. The next prime is 106929083785151. The reversal of 106929083785104 is 401587380929601.

The square root of 106929083785104 is 10340652.

It is a perfect power (a square), and thus also a powerful number.

106929083785104 is a `hidden beast` number, since 1 + 0 + 69 + 29 + 0 + 8 + 37 + 8 + 510 + 4 = 666.

It can be written as a sum of positive squares in only one way, i.e., 105271293632400 + 1657790152704 = 10260180^2 + 1287552^2 .

It is a super-2 number, since 2×106929083785104² (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 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 80 ways as a sum of consecutive naturals, for example, 223233995137 + ... + 223233995615.

It is a 1-persistent number, because it is pandigital, but 2⋅106929083785104 = 213858167570208 is not.

Almost surely, 2^{106929083785104} is an apocalyptic number.

106929083785104 is a gapful number since it is divisible by the number (14) formed by its first and last digit.

106929083785104 is the 10340652-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 106929083785104

106929083785104 is an abundant number, since it is smaller than the sum of its proper divisors (243272350615233).

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

106929083785104 is an frugal number, since it uses more digits than its factorization.

106929083785104 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1500 (or 748 counting only the distinct ones).

The product of its (nonzero) digits is 26127360, while the sum is 63.

The spelling of 106929083785104 in words is "one hundred six trillion, nine hundred twenty-nine billion, eighty-three million, seven hundred eighty-five thousand, one hundred four".