105508032400 has 135 divisors (see below), whose sum is σ = 257558418201. Its totient is φ = 41535383040.

The previous prime is 105508032359. The next prime is 105508032407. The reversal of 105508032400 is 4230805501.

The square root of 105508032400 is 324820.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 13 ways, for example, as 88749176464 + 16758855936 = 297908^2 + 129456^2 .

It is a super-2 number, since 2×105508032400² (a number of 23 digits) contains 22 as substring.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (105508032407) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 708107526 + ... + 708107674.

Almost surely, 2^105508032400 is an apocalyptic number.

105508032400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

105508032400 is the 324820-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105508032400

105508032400 is an abundant number, since it is smaller than the sum of its proper divisors (152050385801).

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

105508032400 is an equidigital number, since it uses as much as digits as its factorization.

105508032400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 534 (or 265 counting only the distinct ones).

The product of its (nonzero) digits is 4800, while the sum is 28.

Adding to 105508032400 its reverse (4230805501), we get a palindrome (109738837901).

The spelling of 105508032400 in words is "one hundred five billion, five hundred eight million, thirty-two thousand, four hundred".