417116160 has 312 divisors, whose sum is σ = 1512910464. Its totient is φ = 106168320.

The previous prime is 417116153. The next prime is 417116171. The reversal of 417116160 is 61611714.

417116160 is a `hidden beast` number, since 41 + 7 + 1 + 1 + 616 + 0 = 666.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 5713884 + ... + 5713956.

It is an arithmetic number, because the mean of its divisors is an integer number (4849072).

Almost surely, 2^417116160 is an apocalyptic number.

417116160 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 417116160, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (756455232).

417116160 is an abundant number, since it is smaller than the sum of its proper divisors (1095794304).

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

417116160 is a wasteful number, since it uses less digits than its factorization.

417116160 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 139 (or 114 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 27.

The square root of 417116160 is about 20423.4218484562. The cubic root of 417116160 is about 747.1692761112.

Adding to 417116160 its reverse (61611714), we get a palindrome (478727874).

The spelling of 417116160 in words is "four hundred seventeen million, one hundred sixteen thousand, one hundred sixty".