417920 has 32 divisors (see below), whose sum is σ = 1000620. Its totient is φ = 166912.

The previous prime is 417899. The next prime is 417931. The reversal of 417920 is 29714.

417920 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 399424 + 18496 = 632^2 + 136^2 .

It is a tau number, because it is divible by the number of its divisors (32).

It is an unprimeable number.

417920 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 314 + ... + 966.

2⁴¹⁷⁹²⁰ is an apocalyptic number.

417920 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 417920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (500310).

417920 is an abundant number, since it is smaller than the sum of its proper divisors (582700).

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

417920 is an equidigital number, since it uses as much as digits as its factorization.

417920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 672 (or 660 counting only the distinct ones).

The product of its (nonzero) digits is 504, while the sum is 23.

The square root of 417920 is about 646.4673232268. The cubic root of 417920 is about 74.7648933982.

The spelling of 417920 in words is "four hundred seventeen thousand, nine hundred twenty".