409920 has 112 divisors (see below), whose sum is σ = 1511808. Its totient is φ = 92160.

The previous prime is 409909. The next prime is 409933. The reversal of 409920 is 29904.

409920 = T₉ + T₁₀ + ... + T₁₃₄.

It is a tau number, because it is divible by the number of its divisors (112).

It is a hoax number, since the sum of its digits (24) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

409920 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 15 ways as a sum of consecutive naturals, for example, 6690 + ... + 6750.

2⁴⁰⁹⁹²⁰ is an apocalyptic number.

409920 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 409920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (755904).

409920 is an abundant number, since it is smaller than the sum of its proper divisors (1101888).

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

409920 is a wasteful number, since it uses less digits than its factorization.

409920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 88 (or 78 counting only the distinct ones).

The product of its (nonzero) digits is 648, while the sum is 24.

The square root of 409920 is about 640.2499511909. The cubic root of 409920 is about 74.2847562570.

The spelling of 409920 in words is "four hundred nine thousand, nine hundred twenty".