414104000 has 112 divisors (see below), whose sum is σ = 1053998400. Its totient is φ = 161049600.

The previous prime is 414103997. The next prime is 414104027. The reversal of 414104000 is 401414.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 295301 + ... + 296699.

It is an arithmetic number, because the mean of its divisors is an integer number (9410700).

Almost surely, 2^414104000 is an apocalyptic number.

414104000 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 414104000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (526999200).

414104000 is an abundant number, since it is smaller than the sum of its proper divisors (639894400).

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

414104000 is a wasteful number, since it uses less digits than its factorization.

414104000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1463 (or 1443 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 14.

The square root of 414104000 is about 20349.5454494689. The cubic root of 414104000 is about 745.3663948548.

Adding to 414104000 its reverse (401414), we get a palindrome (414505414).

The spelling of 414104000 in words is "four hundred fourteen million, one hundred four thousand".