409664 has 28 divisors (see below), whose sum is σ = 839724. Its totient is φ = 198144.

The previous prime is 409657. The next prime is 409691. The reversal of 409664 is 466904.

409664 is nontrivially palindromic in base 7.

It can be written as a sum of positive squares in 2 ways, for example, as 369664 + 40000 = 608^2 + 200^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2282 + ... + 2454.

2⁴⁰⁹⁶⁶⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 409664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (419862).

409664 is an abundant number, since it is smaller than the sum of its proper divisors (430060).

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

409664 is a wasteful number, since it uses less digits than its factorization.

409664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 222 (or 212 counting only the distinct ones).

The product of its (nonzero) digits is 5184, while the sum is 29.

The square root of 409664 is about 640.0499980470. The cubic root of 409664 is about 74.2692891271.

It can be divided in two parts, 4096 and 64, that multiplied together give a 18-th power (262144 = 2¹⁸).

The spelling of 409664 in words is "four hundred nine thousand, six hundred sixty-four".