413145110400 has 288 divisors, whose sum is σ = 1495755958200. Its totient is φ = 100156108800.

The previous prime is 413145110293. The next prime is 413145110449. The reversal of 413145110400 is 4011541314.

It is a happy number.

413145110400 is digitally balanced in base 7, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 983766 + ... + 1339434.

Almost surely, 2^413145110400 is an apocalyptic number.

413145110400 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 413145110400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (747877979100).

413145110400 is an abundant number, since it is smaller than the sum of its proper divisors (1082610847800).

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

413145110400 is a wasteful number, since it uses less digits than its factorization.

413145110400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 355718 (or 355690 counting only the distinct ones).

The product of its (nonzero) digits is 960, while the sum is 24.

Adding to 413145110400 its reverse (4011541314), we get a palindrome (417156651714).

The spelling of 413145110400 in words is "four hundred thirteen billion, one hundred forty-five million, one hundred ten thousand, four hundred".