105313230400 has 567 divisors, whose sum is σ = 323445853107. Its totient is φ = 33646233600.

The previous prime is 105313230389. The next prime is 105313230401. The reversal of 105313230400 is 4032313501.

The square root of 105313230400 is 324520.

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

It can be written as a sum of positive squares in 4 ways, for example, as 48509181504 + 56804048896 = 220248^2 + 238336^2 .

It is a super-2 number, since 2×105313230400² (a number of 23 digits) contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (105313230401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 1726446370 + ... + 1726446430.

Almost surely, 2^105313230400 is an apocalyptic number.

105313230400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

105313230400 is the 324520-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105313230400

105313230400 is an abundant number, since it is smaller than the sum of its proper divisors (218132622707).

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

105313230400 is an equidigital number, since it uses as much as digits as its factorization.

105313230400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 196 (or 94 counting only the distinct ones).

The product of its (nonzero) digits is 1080, while the sum is 22.

Adding to 105313230400 its reverse (4032313501), we get a palindrome (109345543901).

The spelling of 105313230400 in words is "one hundred five billion, three hundred thirteen million, two hundred thirty thousand, four hundred".