414013214400 has 168 divisors, whose sum is σ = 1375503390720. Its totient is φ = 109005911040.

The previous prime is 414013214393. The next prime is 414013214423. The reversal of 414013214400 is 4412310414.

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

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 166704 + ... + 925103.

Almost surely, 2^414013214400 is an apocalyptic number.

414013214400 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 414013214400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (687751695360).

414013214400 is an abundant number, since it is smaller than the sum of its proper divisors (961490176320).

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

414013214400 is a wasteful number, since it uses less digits than its factorization.

414013214400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1091911 (or 1091896 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 24.

Adding to 414013214400 its reverse (4412310414), we get a palindrome (418425524814).

The spelling of 414013214400 in words is "four hundred fourteen billion, thirteen million, two hundred fourteen thousand, four hundred".