105707408400 has 480 divisors, whose sum is σ = 423698595840. Its totient is φ = 24798528000.

The previous prime is 105707408353. The next prime is 105707408407. The reversal of 105707408400 is 4804707501.

105707408400 is a `hidden beast` number, since 1 + 0 + 570 + 7 + 4 + 0 + 84 + 0 + 0 = 666.

It is a super-2 number, since 2×105707408400² (a number of 23 digits) contains 22 as substring.

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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 (105707408407) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 3668449 + ... + 3697151.

It is an arithmetic number, because the mean of its divisors is an integer number (882705408).

Almost surely, 2^105707408400 is an apocalyptic number.

105707408400 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 105707408400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (211849297920).

105707408400 is an abundant number, since it is smaller than the sum of its proper divisors (317991187440).

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

105707408400 is a wasteful number, since it uses less digits than its factorization.

105707408400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 28772 (or 28755 counting only the distinct ones).

The product of its (nonzero) digits is 31360, while the sum is 36.

The spelling of 105707408400 in words is "one hundred five billion, seven hundred seven million, four hundred eight thousand, four hundred".