10505852582400 has 3840 divisors, whose sum is σ = 49022919475200. Its totient is φ = 2149908480000.

The previous prime is 10505852582399. The next prime is 10505852582437. The reversal of 10505852582400 is 428525850501.

10505852582400 is a `hidden beast` number, since 1 + 0 + 5 + 0 + 5 + 8 + 525 + 82 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (3840).

It is a super-2 number, since 2×10505852582400² (a number of 27 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, 104018342350 + ... + 104018342450.

It is an arithmetic number, because the mean of its divisors is an integer number (12766385280).

Almost surely, 2^{10505852582400} is an apocalyptic number.

10505852582400 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 10505852582400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (24511459737600).

10505852582400 is an abundant number, since it is smaller than the sum of its proper divisors (38517066892800).

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

10505852582400 is a wasteful number, since it uses less digits than its factorization.

10505852582400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 268 (or 241 counting only the distinct ones).

The product of its (nonzero) digits is 640000, while the sum is 45.

The spelling of 10505852582400 in words is "ten trillion, five hundred five billion, eight hundred fifty-two million, five hundred eighty-two thousand, four hundred".