414000434000 has 80 divisors (see below), whose sum is σ = 1003502594640. Its totient is φ = 165194956800.

The previous prime is 414000433997. The next prime is 414000434027. The reversal of 414000434000 is 434000414.

It can be written as a sum of positive squares in 8 ways, for example, as 134231373376 + 279769060624 = 366376^2 + 528932^2 .

It is a tau number, because it is divible by the number of its divisors (80).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 564944 + ... + 1071056.

It is an arithmetic number, because the mean of its divisors is an integer number (12543782433).

Almost surely, 2^414000434000 is an apocalyptic number.

414000434000 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 414000434000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (501751297320).

414000434000 is an abundant number, since it is smaller than the sum of its proper divisors (589502160640).

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

414000434000 is a wasteful number, since it uses less digits than its factorization.

414000434000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 506545 (or 506529 counting only the distinct ones).

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

Adding to 414000434000 its reverse (434000414), we get a palindrome (414434434414).

The spelling of 414000434000 in words is "four hundred fourteen billion, four hundred thirty-four thousand".