408400048800 has 432 divisors, whose sum is σ = 1478366737848. Its totient is φ = 106025779200.

The previous prime is 408400048789. The next prime is 408400048801. The reversal of 408400048800 is 8840004804.

It can be written as a sum of positive squares in 12 ways, for example, as 1167178896 + 407232869904 = 34164^2 + 638148^2 .

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

It is not an unprimeable number, because it can be changed into a prime (408400048801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 175052434 + ... + 175054766.

Almost surely, 2^408400048800 is an apocalyptic number.

408400048800 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 408400048800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (739183368924).

408400048800 is an abundant number, since it is smaller than the sum of its proper divisors (1069966689048).

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

408400048800 is a wasteful number, since it uses less digits than its factorization.

408400048800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2993 (or 2977 counting only the distinct ones).

The product of its (nonzero) digits is 32768, while the sum is 36.

The spelling of 408400048800 in words is "four hundred eight billion, four hundred million, forty-eight thousand, eight hundred".