417288960 has 432 divisors, whose sum is σ = 1635772320. Its totient is φ = 97320960.

The previous prime is 417288959. The next prime is 417289007. The reversal of 417288960 is 69882714.

It is a super-2 number, since 2×417288960² = 348260152275763200, which contains 22 as substring.

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

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 4688596 + ... + 4688684.

It is an arithmetic number, because the mean of its divisors is an integer number (3786510).

Almost surely, 2^417288960 is an apocalyptic number.

417288960 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 417288960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (817886160).

417288960 is an abundant number, since it is smaller than the sum of its proper divisors (1218483360).

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

417288960 is a wasteful number, since it uses less digits than its factorization.

417288960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 164 (or 147 counting only the distinct ones).

The product of its (nonzero) digits is 193536, while the sum is 45.

The square root of 417288960 is about 20427.6518474346. The cubic root of 417288960 is about 747.2724392413.

It can be divided in two parts, 4 and 17288960, that added together give a square (17288964 = 4158²).

The spelling of 417288960 in words is "four hundred seventeen million, two hundred eighty-eight thousand, nine hundred sixty".