415406030400 has 567 divisors, whose sum is σ = 1524980835859. Its totient is φ = 107248128000.

The previous prime is 415406030363. The next prime is 415406030423. The reversal of 415406030400 is 4030604514.

The square root of 415406030400 is 644520.

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

415406030400 is a `hidden beast` number, since 4 + 1 + 54 + 0 + 603 + 0 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 174851095104 + 240554935296 = 418152^2 + 490464^2 .

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 3171038335 + ... + 3171038465.

Almost surely, 2^415406030400 is an apocalyptic number.

415406030400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

415406030400 is the 644520-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 415406030400

415406030400 is an abundant number, since it is smaller than the sum of its proper divisors (1109574805459).

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

415406030400 is a wasteful number, since it uses less digits than its factorization.

415406030400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 372 (or 182 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 27.

Adding to 415406030400 its reverse (4030604514), we get a palindrome (419436634914).

The spelling of 415406030400 in words is "four hundred fifteen billion, four hundred six million, thirty thousand, four hundred".