413413144185600 has 1944 divisors, whose sum is σ = 1664009283256320. Its totient is φ = 101503091589120.

The previous prime is 413413144185593. The next prime is 413413144185611. The reversal of 413413144185600 is 6581441314314.

413413144185600 is a `hidden beast` number, since 4 + 1 + 3 + 4 + 1 + 31 + 4 + 4 + 1 + 8 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1944).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 115381841409 + ... + 115381844991.

Almost surely, 2^{413413144185600} is an apocalyptic number.

413413144185600 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 413413144185600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (832004641628160).

413413144185600 is an abundant number, since it is smaller than the sum of its proper divisors (1250596139070720).

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

413413144185600 is a wasteful number, since it uses less digits than its factorization.

413413144185600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4089 (or 4045 counting only the distinct ones).

The product of its (nonzero) digits is 552960, while the sum is 45.

Adding to 413413144185600 its reverse (6581441314314), we get a palindrome (419994585499914).

The spelling of 413413144185600 in words is "four hundred thirteen trillion, four hundred thirteen billion, one hundred forty-four million, one hundred eighty-five thousand, six hundred".