414024401400 has 192 divisors, whose sum is σ = 1302179155200. Its totient is φ = 108804264960.

The previous prime is 414024401389. The next prime is 414024401407. The reversal of 414024401400 is 4104420414.

It is a happy number.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414024401407) 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 47 ways as a sum of consecutive naturals, for example, 20358037 + ... + 20378363.

It is an arithmetic number, because the mean of its divisors is an integer number (6782183100).

Almost surely, 2^414024401400 is an apocalyptic number.

414024401400 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 414024401400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (651089577600).

414024401400 is an abundant number, since it is smaller than the sum of its proper divisors (888154753800).

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

414024401400 is a wasteful number, since it uses less digits than its factorization.

414024401400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 20838 (or 20829 counting only the distinct ones).

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

Adding to 414024401400 its reverse (4104420414), we get a palindrome (418128821814).

The spelling of 414024401400 in words is "four hundred fourteen billion, twenty-four million, four hundred one thousand, four hundred".