414345716000 has 96 divisors (see below), whose sum is σ = 1018301527152. Its totient is φ = 165696921600.

The previous prime is 414345715991. The next prime is 414345716003. The reversal of 414345716000 is 617543414.

It can be written as a sum of positive squares in 8 ways, for example, as 68662865296 + 345682850704 = 262036^2 + 587948^2 .

It is not an unprimeable number, because it can be changed into a prime (414345716003) 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 15 ways as a sum of consecutive naturals, for example, 19817552 + ... + 19838448.

Almost surely, 2^414345716000 is an apocalyptic number.

414345716000 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 414345716000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (509150763576).

414345716000 is an abundant number, since it is smaller than the sum of its proper divisors (603955811152).

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

414345716000 is a wasteful number, since it uses less digits than its factorization.

414345716000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 25879 (or 25861 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 35.

The spelling of 414345716000 in words is "four hundred fourteen billion, three hundred forty-five million, seven hundred sixteen thousand".