409320 has 64 divisors (see below), whose sum is σ = 1368000. Its totient is φ = 108864.

The previous prime is 409291. The next prime is 409327. The reversal of 409320 is 23904.

It is a super-3 number, since 3×409320³ = 205735933312704000, which contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 409293 and 409302.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 409320.

It is not an unprimeable number, because it can be changed into a prime (409327) by changing a digit.

409320 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 (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 891 + ... + 1269.

It is an arithmetic number, because the mean of its divisors is an integer number (21375).

2⁴⁰⁹³²⁰ is an apocalyptic number.

409320 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 409320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (684000).

409320 is an abundant number, since it is smaller than the sum of its proper divisors (958680).

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

409320 is a wasteful number, since it uses less digits than its factorization.

409320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 399 (or 389 counting only the distinct ones).

The product of its (nonzero) digits is 216, while the sum is 18.

The square root of 409320 is about 639.7812126032. The cubic root of 409320 is about 74.2484950210.

It can be divided in two parts, 409 and 320, that added together give a 6-th power (729 = 3⁶).

The spelling of 409320 in words is "four hundred nine thousand, three hundred twenty".