414404400 has 120 divisors (see below), whose sum is σ = 1336850944. Its totient is φ = 109728000.

The previous prime is 414404369. The next prime is 414404413. The reversal of 414404400 is 4404414.

It is a tau number, because it is divible by the number of its divisors (120).

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, 180057 + ... + 182343.

Almost surely, 2^414404400 is an apocalyptic number.

414404400 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 414404400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (668425472).

414404400 is an abundant number, since it is smaller than the sum of its proper divisors (922446544).

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

414404400 is a wasteful number, since it uses less digits than its factorization.

414404400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2459 (or 2448 counting only the distinct ones).

The product of its (nonzero) digits is 1024, while the sum is 21.

The square root of 414404400 is about 20356.9251116174. The cubic root of 414404400 is about 745.5465862594.

Adding to 414404400 its reverse (4404414), we get a palindrome (418808814).

The spelling of 414404400 in words is "four hundred fourteen million, four hundred four thousand, four hundred".