415032400 has 60 divisors (see below), whose sum is σ = 1015980732. Its totient is φ = 162872320.

The previous prime is 415032391. The next prime is 415032461. The reversal of 415032400 is 4230514.

It can be written as a sum of positive squares in 6 ways, for example, as 25522704 + 389509696 = 5052^2 + 19736^2 .

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 11412 + ... + 30988.

Almost surely, 2^415032400 is an apocalyptic number.

415032400 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 415032400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (507990366).

415032400 is an abundant number, since it is smaller than the sum of its proper divisors (600948332).

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

415032400 is a wasteful number, since it uses less digits than its factorization.

415032400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 19648 (or 19637 counting only the distinct ones).

The product of its (nonzero) digits is 480, while the sum is 19.

The square root of 415032400 is about 20372.3439986664. The cubic root of 415032400 is about 745.9230035510.

Adding to 415032400 its reverse (4230514), we get a palindrome (419262914).

The spelling of 415032400 in words is "four hundred fifteen million, thirty-two thousand, four hundred".