414998400 has 192 divisors, whose sum is σ = 1381161600. Its totient is φ = 109516800.

The previous prime is 414998383. The next prime is 414998411. The reversal of 414998400 is 4899414.

It is a tau number, because it is divible by the number of its divisors (192).

It is a congruent number.

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, 1334245 + ... + 1334555.

It is an arithmetic number, because the mean of its divisors is an integer number (7193550).

Almost surely, 2^414998400 is an apocalyptic number.

414998400 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 414998400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (690580800).

414998400 is an abundant number, since it is smaller than the sum of its proper divisors (966163200).

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

414998400 is a wasteful number, since it uses less digits than its factorization.

414998400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 477 (or 460 counting only the distinct ones).

The product of its (nonzero) digits is 41472, while the sum is 39.

The square root of 414998400 is about 20371.5095169700. The cubic root of 414998400 is about 745.9026339970.

The spelling of 414998400 in words is "four hundred fourteen million, nine hundred ninety-eight thousand, four hundred".