413616441600 has 648 divisors, whose sum is σ = 1561894719840. Its totient is φ = 104137850880.

The previous prime is 413616441571. The next prime is 413616441607. The reversal of 413616441600 is 6144616314.

413616441600 is a `hidden beast` number, since 4 + 1 + 3 + 6 + 1 + 6 + 4 + 41 + 600 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (413616441607) by changing a digit.

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 71 ways as a sum of consecutive naturals, for example, 500140387 + ... + 500141213.

Almost surely, 2^413616441600 is an apocalyptic number.

413616441600 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 413616441600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (780947359920).

413616441600 is an abundant number, since it is smaller than the sum of its proper divisors (1148278278240).

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

413616441600 is a wasteful number, since it uses less digits than its factorization.

413616441600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1335 (or 1313 counting only the distinct ones).

The product of its (nonzero) digits is 41472, while the sum is 36.

The spelling of 413616441600 in words is "four hundred thirteen billion, six hundred sixteen million, four hundred forty-one thousand, six hundred".