10505271313800 has 576 divisors, whose sum is σ = 37047405957120. Its totient is φ = 2664446400000.

The previous prime is 10505271313799. The next prime is 10505271313807. The reversal of 10505271313800 is 831317250501.

It is a happy number.

10505271313800 is a `hidden beast` number, since 1 + 0 + 5 + 0 + 5 + 271 + 3 + 1 + 380 + 0 = 666.

10505271313800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a super-2 number, since 2×10505271313800² (a number of 27 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (10505271313807) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 1311351795 + ... + 1311359805.

It is an arithmetic number, because the mean of its divisors is an integer number (64318413120).

Almost surely, 2^{10505271313800} is an apocalyptic number.

10505271313800 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 10505271313800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (18523702978560).

10505271313800 is an abundant number, since it is smaller than the sum of its proper divisors (26542134643320).

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

10505271313800 is a wasteful number, since it uses less digits than its factorization.

10505271313800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 8466 (or 8454 counting only the distinct ones).

The product of its (nonzero) digits is 25200, while the sum is 36.

The spelling of 10505271313800 in words is "ten trillion, five hundred five billion, two hundred seventy-one million, three hundred thirteen thousand, eight hundred".