413575200 has 288 divisors, whose sum is σ = 1535526720. Its totient is φ = 107366400.

The previous prime is 413575199. The next prime is 413575237. The reversal of 413575200 is 2575314.

It is a happy number.

413575200 is a `hidden beast` number, since 4 + 135 + 7 + 520 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 885367 + ... + 885833.

It is an arithmetic number, because the mean of its divisors is an integer number (5331690).

Almost surely, 2^413575200 is an apocalyptic number.

413575200 is a gapful number since it is divisible by the number (40) 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 413575200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (767763360).

413575200 is an abundant number, since it is smaller than the sum of its proper divisors (1121951520).

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

413575200 is a wasteful number, since it uses less digits than its factorization.

413575200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 537 (or 518 counting only the distinct ones).

The product of its (nonzero) digits is 4200, while the sum is 27.

The square root of 413575200 is about 20336.5483797030. The cubic root of 413575200 is about 745.0489885658.

The spelling of 413575200 in words is "four hundred thirteen million, five hundred seventy-five thousand, two hundred".