414342400 has 108 divisors (see below), whose sum is σ = 1037332044. Its totient is φ = 163840000.

The previous prime is 414342371. The next prime is 414342403. The reversal of 414342400 is 4243414.

It can be written as a sum of positive squares in 6 ways, for example, as 58491904 + 355850496 = 7648^2 + 18864^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414342403) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 646080 + ... + 646720.

Almost surely, 2^414342400 is an apocalyptic number.

414342400 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 414342400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (518666022).

414342400 is an abundant number, since it is smaller than the sum of its proper divisors (622989644).

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

414342400 is a wasteful number, since it uses less digits than its factorization.

414342400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 768 (or 749 counting only the distinct ones).

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

The square root of 414342400 is about 20355.4022313488. The cubic root of 414342400 is about 745.5094034224.

Adding to 414342400 its reverse (4243414), we get a palindrome (418585814).

It can be divided in two parts, 41434 and 2400, that added together give a palindrome (43834).

The spelling of 414342400 in words is "four hundred fourteen million, three hundred forty-two thousand, four hundred".