413400960000 has 660 divisors, whose sum is σ = 1704886724112. Its totient is φ = 94482432000.

The previous prime is 413400959941. The next prime is 413400960001. The reversal of 413400960000 is 69004314.

413400960000 is a `hidden beast` number, since 4 + 13 + 40 + 0 + 9 + 600 + 0 + 0 = 666.

It is not an unprimeable number, because it can be changed into a prime (413400960001) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 40314874 + ... + 40325126.

Almost surely, 2^413400960000 is an apocalyptic number.

413400960000 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 413400960000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (852443362056).

413400960000 is an abundant number, since it is smaller than the sum of its proper divisors (1291485764112).

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

413400960000 is a wasteful number, since it uses less digits than its factorization.

413400960000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 10306 (or 10270 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 27.

Adding to 413400960000 its reverse (69004314), we get a palindrome (413469964314).

The spelling of 413400960000 in words is "four hundred thirteen billion, four hundred million, nine hundred sixty thousand".