105507164528640 has 2688 divisors, whose sum is σ = 447790641120000. Its totient is φ = 23493945065472.

The previous prime is 105507164528611. The next prime is 105507164528761. The reversal of 105507164528640 is 46825461705501.

105507164528640 is a `hidden beast` number, since 1 + 0 + 5 + 5 + 0 + 71 + 6 + 4 + 528 + 6 + 40 = 666.

It is a tau number, because it is divible by the number of its divisors (2688).

It is a super-2 number, since 2×105507164528640² (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 an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 589425500071 + ... + 589425500249.

Almost surely, 2^{105507164528640} is an apocalyptic number.

105507164528640 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 105507164528640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (223895320560000).

105507164528640 is an abundant number, since it is smaller than the sum of its proper divisors (342283476591360).

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

105507164528640 is a wasteful number, since it uses less digits than its factorization.

105507164528640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 455 (or 418 counting only the distinct ones).

The product of its (nonzero) digits is 8064000, while the sum is 54.

The spelling of 105507164528640 in words is "one hundred five trillion, five hundred seven billion, one hundred sixty-four million, five hundred twenty-eight thousand, six hundred forty".