412448400 has 360 divisors, whose sum is σ = 1763012160. Its totient is φ = 86952960.

The previous prime is 412448381. The next prime is 412448401. The reversal of 412448400 is 4844214.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (360).

It is a super-2 number, since 2×412448400² = 340227365325120000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (412448401) by changing a digit.

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 71 ways as a sum of consecutive naturals, for example, 326971 + ... + 328229.

It is an arithmetic number, because the mean of its divisors is an integer number (4897256).

Almost surely, 2^412448400 is an apocalyptic number.

412448400 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 412448400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (881506080).

412448400 is an abundant number, since it is smaller than the sum of its proper divisors (1350563760).

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

412448400 is a wasteful number, since it uses less digits than its factorization.

412448400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1303 (or 1289 counting only the distinct ones).

The product of its (nonzero) digits is 4096, while the sum is 27.

The square root of 412448400 is about 20308.8256676746. The cubic root of 412448400 is about 744.3717358426.

The spelling of 412448400 in words is "four hundred twelve million, four hundred forty-eight thousand, four hundred".