414234400 has 72 divisors (see below), whose sum is σ = 1043933184. Its totient is φ = 160339200.

The previous prime is 414234341. The next prime is 414234449. The reversal of 414234400 is 4432414.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 16449 + ... + 33151.

It is an arithmetic number, because the mean of its divisors is an integer number (14499072).

Almost surely, 2^414234400 is an apocalyptic number.

414234400 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 414234400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (521966592).

414234400 is an abundant number, since it is smaller than the sum of its proper divisors (629698784).

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

414234400 is a wasteful number, since it uses less digits than its factorization.

414234400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 16754 (or 16741 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 22.

The square root of 414234400 is about 20352.7492000467. The cubic root of 414234400 is about 745.4446244601. Note that the first 3 decimals are identical.

Adding to 414234400 its reverse (4432414), we get a palindrome (418666814).

The spelling of 414234400 in words is "four hundred fourteen million, two hundred thirty-four thousand, four hundred".