414012404040 has 256 divisors, whose sum is σ = 1290885120000. Its totient is φ = 106113162240.

The previous prime is 414012404011. The next prime is 414012404063. The reversal of 414012404040 is 40404210414.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a self number, because there is not a number n which added to its sum of digits gives 414012404040.

It is an unprimeable number.

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 63 ways as a sum of consecutive naturals, for example, 450502701 + ... + 450503619.

It is an arithmetic number, because the mean of its divisors is an integer number (5042520000).

Almost surely, 2^414012404040 is an apocalyptic number.

414012404040 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 414012404040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (645442560000).

414012404040 is an abundant number, since it is smaller than the sum of its proper divisors (876872715960).

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

414012404040 is a wasteful number, since it uses less digits than its factorization.

414012404040 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1660 (or 1656 counting only the distinct ones).

The product of its (nonzero) digits is 2048, while the sum is 24.

Adding to 414012404040 its reverse (40404210414), we get a palindrome (454416614454).

The spelling of 414012404040 in words is "four hundred fourteen billion, twelve million, four hundred four thousand, forty".