414024320000 has 110 divisors (see below), whose sum is σ = 1034225940198. Its totient is φ = 165609472000.

The previous prime is 414024319991. The next prime is 414024320051. The reversal of 414024320000 is 23420414.

It can be written as a sum of positive squares in 5 ways, for example, as 162389656576 + 251634663424 = 402976^2 + 501632^2 .

It is a super-2 number, since 2×414024320000² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (20).

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 9 ways as a sum of consecutive naturals, for example, 316544 + ... + 963456.

Almost surely, 2^414024320000 is an apocalyptic number.

414024320000 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 414024320000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (517112970099).

414024320000 is an abundant number, since it is smaller than the sum of its proper divisors (620201620198).

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

414024320000 is an frugal number, since it uses more digits than its factorization.

414024320000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 646953 (or 646920 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 20.

Adding to 414024320000 its reverse (23420414), we get a palindrome (414047740414).

The spelling of 414024320000 in words is "four hundred fourteen billion, twenty-four million, three hundred twenty thousand".