414030400 has 126 divisors (see below), whose sum is σ = 1185328338. Its totient is φ = 141926400.

The previous prime is 414030391. The next prime is 414030413. The reversal of 414030400 is 4030414.

It can be written as a sum of positive squares in 3 ways, for example, as 802816 + 413227584 = 896^2 + 20328^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 75760 + ... + 81040.

Almost surely, 2^414030400 is an apocalyptic number.

414030400 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 414030400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (592664169).

414030400 is an abundant number, since it is smaller than the sum of its proper divisors (771297938).

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

414030400 is a wasteful number, since it uses less digits than its factorization.

414030400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5317 (or 5295 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 16.

The square root of 414030400 is about 20347.7369749071. The cubic root of 414030400 is about 745.3222334709.

Adding to 414030400 its reverse (4030414), we get a palindrome (418060814).

The spelling of 414030400 in words is "four hundred fourteen million, thirty thousand, four hundred".