409680 has 60 divisors (see below), whose sum is σ = 1378260. Its totient is φ = 109056.

The previous prime is 409657. The next prime is 409691. The reversal of 409680 is 86904.

It can be written as a sum of positive squares in 2 ways, for example, as 104976 + 304704 = 324^2 + 552^2 .

It is a tau number, because it is divible by the number of its divisors (60).

It is a congruent number.

It is an unprimeable 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 11 ways as a sum of consecutive naturals, for example, 436 + ... + 1004.

It is an arithmetic number, because the mean of its divisors is an integer number (22971).

2⁴⁰⁹⁶⁸⁰ is an apocalyptic number.

409680 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 409680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (689130).

409680 is an abundant number, since it is smaller than the sum of its proper divisors (968580).

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

409680 is a wasteful number, since it uses less digits than its factorization.

409680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 588 (or 579 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 409680 is about 640.0624969485. The cubic root of 409680 is about 74.2702560114.

It can be divided in two parts, 409 and 680, that added together give a square (1089 = 33²).

The spelling of 409680 in words is "four hundred nine thousand, six hundred eighty".