413224800 has 144 divisors (see below), whose sum is σ = 1354413312. Its totient is φ = 109427200.

The previous prime is 413224783. The next prime is 413224873. The reversal of 413224800 is 8422314.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 400285 + ... + 401315.

It is an arithmetic number, because the mean of its divisors is an integer number (9405648).

Almost surely, 2^413224800 is an apocalyptic number.

413224800 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 413224800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (677206656).

413224800 is an abundant number, since it is smaller than the sum of its proper divisors (941188512).

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

413224800 is a wasteful number, since it uses less digits than its factorization.

413224800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1221 (or 1208 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 24.

The square root of 413224800 is about 20327.9315229071. The cubic root of 413224800 is about 744.8385158157.

The spelling of 413224800 in words is "four hundred thirteen million, two hundred twenty-four thousand, eight hundred".