417889920 has 512 divisors, whose sum is σ = 1692057600. Its totient is φ = 85524480.

The previous prime is 417889919. The next prime is 417889943. The reversal of 417889920 is 29988714.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 417889920.

It is a congruent number.

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 63 ways as a sum of consecutive naturals, for example, 7082851 + ... + 7082909.

It is an arithmetic number, because the mean of its divisors is an integer number (3304800).

Almost surely, 2^417889920 is an apocalyptic number.

417889920 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 417889920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (846028800).

417889920 is an abundant number, since it is smaller than the sum of its proper divisors (1274167680).

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

417889920 is a wasteful number, since it uses less digits than its factorization.

417889920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 136 (or 124 counting only the distinct ones).

The product of its (nonzero) digits is 290304, while the sum is 48.

The square root of 417889920 is about 20442.3560285991. The cubic root of 417889920 is about 747.6309960837.

The spelling of 417889920 in words is "four hundred seventeen million, eight hundred eighty-nine thousand, nine hundred twenty".