412448000 has 72 divisors (see below), whose sum is σ = 1027539240. Its totient is φ = 164966400.

The previous prime is 412447993. The next prime is 412448009. The reversal of 412448000 is 844214.

It can be written as a sum of positive squares in 4 ways, for example, as 7311616 + 405136384 = 2704^2 + 20128^2 .

It is a super-2 number, since 2×412448000² = 340226705408000000, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (412448009) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 25556 + ... + 38444.

Almost surely, 2^412448000 is an apocalyptic number.

412448000 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 412448000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (513769620).

412448000 is an abundant number, since it is smaller than the sum of its proper divisors (615091240).

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

412448000 is an equidigital number, since it uses as much as digits as its factorization.

412448000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 12920 (or 12896 counting only the distinct ones).

The product of its (nonzero) digits is 1024, while the sum is 23.

The square root of 412448000 is about 20308.8158197370. The cubic root of 412448000 is about 744.3714952074.

The spelling of 412448000 in words is "four hundred twelve million, four hundred forty-eight thousand".