414340000000 has 144 divisors (see below), whose sum is σ = 1033874111088. Its totient is φ = 165728000000.

The previous prime is 414339999991. The next prime is 414340000001. The reversal of 414340000000 is 43414.

It can be written as a sum of positive squares in 8 ways, for example, as 194671558656 + 219668441344 = 441216^2 + 468688^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is not an unprimeable number, because it can be changed into a prime (414340000001) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 19989642 + ... + 20010358.

It is an arithmetic number, because the mean of its divisors is an integer number (7179681327).

Almost surely, 2^414340000000 is an apocalyptic number.

414340000000 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 414340000000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (516937055544).

414340000000 is an abundant number, since it is smaller than the sum of its proper divisors (619534111088).

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

414340000000 is an frugal number, since it uses more digits than its factorization.

414340000000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 20768 (or 20724 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 16.

Adding to 414340000000 its reverse (43414), we get a palindrome (414340043414).

The spelling of 414340000000 in words is "four hundred fourteen billion, three hundred forty million", and thus it is an aban number.