413798400 has 234 divisors, whose sum is σ = 1485437850. Its totient is φ = 110100480.

The previous prime is 413798353. The next prime is 413798423. The reversal of 413798400 is 4897314.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 37748736 + 376049664 = 6144^2 + 19392^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 921376 + ... + 921824.

It is an arithmetic number, because the mean of its divisors is an integer number (6348025).

Almost surely, 2^413798400 is an apocalyptic number.

413798400 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 413798400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (742718925).

413798400 is an abundant number, since it is smaller than the sum of its proper divisors (1071639450).

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

413798400 is a wasteful number, since it uses less digits than its factorization.

413798400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 489 (or 459 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The square root of 413798400 is about 20342.0352964004. The cubic root of 413798400 is about 745.1829948502.

The spelling of 413798400 in words is "four hundred thirteen million, seven hundred ninety-eight thousand, four hundred".