413074400 has 72 divisors (see below), whose sum is σ = 1020731544. Its totient is φ = 163212800.

The previous prime is 413074373. The next prime is 413074427. The reversal of 413074400 is 4470314.

It is an interprime number because it is at equal distance from previous prime (413074373) and next prime (413074427).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 63290 + ... + 69510.

It is an arithmetic number, because the mean of its divisors is an integer number (14176827).

Almost surely, 2^413074400 is an apocalyptic number.

413074400 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 413074400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (510365772).

413074400 is an abundant number, since it is smaller than the sum of its proper divisors (607657144).

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

413074400 is a wasteful number, since it uses less digits than its factorization.

413074400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6324 (or 6311 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 23.

The square root of 413074400 is about 20324.2318428028. The cubic root of 413074400 is about 744.7481394181.

The spelling of 413074400 in words is "four hundred thirteen million, seventy-four thousand, four hundred".