413178400 has 72 divisors (see below), whose sum is σ = 1032215184. Its totient is φ = 161414400.

The previous prime is 413178391. The next prime is 413178401. The reversal of 413178400 is 4871314.

It is not an unprimeable number, because it can be changed into a prime (413178401) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 28395 + ... + 40405.

It is an arithmetic number, because the mean of its divisors is an integer number (14336322).

Almost surely, 2^413178400 is an apocalyptic number.

413178400 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 413178400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (516107592).

413178400 is an abundant number, since it is smaller than the sum of its proper divisors (619036784).

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

413178400 is a wasteful number, since it uses less digits than its factorization.

413178400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 12074 (or 12061 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 28.

The square root of 413178400 is about 20326.7902040632. The cubic root of 413178400 is about 744.8106360750.

The spelling of 413178400 in words is "four hundred thirteen million, one hundred seventy-eight thousand, four hundred".