414430014414000 has 960 divisors, whose sum is σ = 1533172128703488. Its totient is φ = 95933859840000.

The previous prime is 414430014413999. The next prime is 414430014414037. The reversal of 414430014414000 is 414410034414.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 22461104775 + ... + 22461123225.

Almost surely, 2^{414430014414000} is an apocalyptic number.

414430014414000 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 414430014414000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (766586064351744).

414430014414000 is an abundant number, since it is smaller than the sum of its proper divisors (1118742114289488).

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

414430014414000 is a wasteful number, since it uses less digits than its factorization.

414430014414000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 19823 (or 19794 counting only the distinct ones).

The product of its (nonzero) digits is 12288, while the sum is 30.

Adding to 414430014414000 its reverse (414410034414), we get a palindrome (414844424448414).

The spelling of 414430014414000 in words is "four hundred fourteen trillion, four hundred thirty billion, fourteen million, four hundred fourteen thousand".