417320064 has 144 divisors (see below), whose sum is σ = 1397133270. Its totient is φ = 119218176.

The previous prime is 417319999. The next prime is 417320081. The reversal of 417320064 is 460023714.

It can be written as a sum of positive squares in only one way, i.e., 399680064 + 17640000 = 19992^2 + 4200^2 .

It is a tau number, because it is divible by the number of its divisors (144).

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 52752 + ... + 60144.

Almost surely, 2^417320064 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 417320064, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (698566635).

417320064 is an abundant number, since it is smaller than the sum of its proper divisors (979813206).

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

417320064 is a wasteful number, since it uses less digits than its factorization.

417320064 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7427 (or 7405 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 27.

The square root of 417320064 is about 20428.4131542320. The cubic root of 417320064 is about 747.2910055799.

Adding to 417320064 its reverse (460023714), we get a palindrome (877343778).

The spelling of 417320064 in words is "four hundred seventeen million, three hundred twenty thousand, sixty-four".