106505635384800 has 288 divisors, whose sum is σ = 385838492256000. Its totient is φ = 28354084462080.

The previous prime is 106505635384711. The next prime is 106505635384831. The reversal of 106505635384800 is 8483536505601.

It is a happy number.

106505635384800 is a `hidden beast` number, since 1 + 0 + 6 + 5 + 0 + 5 + 63 + 538 + 48 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×106505635384800² (a number of 29 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 an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 8822527 + ... + 17054273.

It is an arithmetic number, because the mean of its divisors is an integer number (1339716987000).

Almost surely, 2^{106505635384800} is an apocalyptic number.

106505635384800 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 106505635384800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (192919246128000).

106505635384800 is an abundant number, since it is smaller than the sum of its proper divisors (279332856871200).

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

106505635384800 is a wasteful number, since it uses less digits than its factorization.

106505635384800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 8232375 (or 8232356 counting only the distinct ones).

The product of its (nonzero) digits is 10368000, while the sum is 54.

The spelling of 106505635384800 in words is "one hundred six trillion, five hundred five billion, six hundred thirty-five million, three hundred eighty-four thousand, eight hundred".