417130560 has 840 divisors, whose sum is σ = 1962058560. Its totient is φ = 82114560.

The previous prime is 417130477. The next prime is 417130601. The reversal of 417130560 is 65031714.

417130560 is a `hidden beast` number, since 4 + 1 + 71 + 30 + 560 = 666.

It is a tau number, because it is divible by the number of its divisors (840).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 21954231 + ... + 21954249.

It is an arithmetic number, because the mean of its divisors is an integer number (2335784).

Almost surely, 2^417130560 is an apocalyptic number.

417130560 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 417130560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (981029280).

417130560 is an abundant number, since it is smaller than the sum of its proper divisors (1544928000).

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

417130560 is a wasteful number, since it uses less digits than its factorization.

417130560 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 77 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 2520, while the sum is 27.

The square root of 417130560 is about 20423.7743818326. The cubic root of 417130560 is about 747.1778741268.

The spelling of 417130560 in words is "four hundred seventeen million, one hundred thirty thousand, five hundred sixty".