105144115564800 has 3456 divisors, whose sum is σ = 468748623168000. Its totient is φ = 23064218173440.

The previous prime is 105144115564769. The next prime is 105144115564823. The reversal of 105144115564800 is 8465511441501.

105144115564800 is a `hidden beast` number, since 1 + 0 + 5 + 1 + 4 + 4 + 1 + 1 + 5 + 564 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (3456).

It is a super-2 number, since 2×105144115564800² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 58772562306 + ... + 58772564094.

Almost surely, 2^{105144115564800} is an apocalyptic number.

105144115564800 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 105144115564800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (234374311584000).

105144115564800 is an abundant number, since it is smaller than the sum of its proper divisors (363604507603200).

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

105144115564800 is a wasteful number, since it uses less digits than its factorization.

105144115564800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1885 (or 1848 counting only the distinct ones).

The product of its (nonzero) digits is 384000, while the sum is 45.

The spelling of 105144115564800 in words is "one hundred five trillion, one hundred forty-four billion, one hundred fifteen million, five hundred sixty-four thousand, eight hundred".