413715600 has 225 divisors, whose sum is σ = 1498048123. Its totient is φ = 109347840.

The previous prime is 413715593. The next prime is 413715619. The reversal of 413715600 is 6517314.

The square root of 413715600 is 20340.

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

413715600 is a `hidden beast` number, since 41 + 3 + 7 + 15 + 600 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 210482064 + 203233536 = 14508^2 + 14256^2 .

It is a tau number, because it is divible by the number of its divisors (225).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 3661144 + ... + 3661256.

Almost surely, 2^413715600 is an apocalyptic number.

413715600 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

413715600 is the 20340-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413715600

413715600 is an abundant number, since it is smaller than the sum of its proper divisors (1084332523).

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

413715600 is a wasteful number, since it uses less digits than its factorization.

413715600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 256 (or 123 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The cubic root of 413715600 is about 745.1332884651.

It can be divided in two parts, 41371 and 5600, that added together give a triangular number (46971 = T₃₀₆).

The spelling of 413715600 in words is "four hundred thirteen million, seven hundred fifteen thousand, six hundred".