414431200000 has 216 divisors, whose sum is σ = 1036864417680. Its totient is φ = 165312000000.

The previous prime is 414431199989. The next prime is 414431200019. The reversal of 414431200000 is 2134414.

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 23 ways as a sum of consecutive naturals, for example, 560799631 + ... + 560800369.

It is an arithmetic number, because the mean of its divisors is an integer number (4800298230).

Almost surely, 2^414431200000 is an apocalyptic number.

414431200000 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 414431200000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (518432208840).

414431200000 is an abundant number, since it is smaller than the sum of its proper divisors (622433217680).

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

414431200000 is an frugal number, since it uses more digits than its factorization.

414431200000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1481 (or 1447 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 19.

Adding to 414431200000 its reverse (2134414), we get a palindrome (414433334414).

The spelling of 414431200000 in words is "four hundred fourteen billion, four hundred thirty-one million, two hundred thousand".