415410400 has 72 divisors (see below), whose sum is σ = 1017684864. Its totient is φ = 165580800.

The previous prime is 415410397. The next prime is 415410409. The reversal of 415410400 is 4014514.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415410409) 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, 281665 + ... + 283135.

It is an arithmetic number, because the mean of its divisors is an integer number (14134512).

Almost surely, 2^415410400 is an apocalyptic number.

415410400 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 415410400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (508842432).

415410400 is an abundant number, since it is smaller than the sum of its proper divisors (602274464).

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

415410400 is a wasteful number, since it uses less digits than its factorization.

415410400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1844 (or 1831 counting only the distinct ones).

The product of its (nonzero) digits is 320, while the sum is 19.

The square root of 415410400 is about 20381.6191702230. The cubic root of 415410400 is about 746.1493901645.

Adding to 415410400 its reverse (4014514), we get a palindrome (419424914).

The spelling of 415410400 in words is "four hundred fifteen million, four hundred ten thousand, four hundred".