414400896 has 384 divisors, whose sum is σ = 1514822400. Its totient is φ = 105836544.

The previous prime is 414400871. The next prime is 414400939. The reversal of 414400896 is 698004414.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a self number, because there is not a number n which added to its sum of digits gives 414400896.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 6185055 + ... + 6185121.

It is an arithmetic number, because the mean of its divisors is an integer number (3944850).

Almost surely, 2^414400896 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414400896, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (757411200).

414400896 is an abundant number, since it is smaller than the sum of its proper divisors (1100421504).

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

414400896 is a wasteful number, since it uses less digits than its factorization.

414400896 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 166 (or 151 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 414400896 is about 20356.8390473570. The cubic root of 414400896 is about 745.5444849282.

The spelling of 414400896 in words is "four hundred fourteen million, four hundred thousand, eight hundred ninety-six".