409600 has 45 divisors (see below), whose sum is σ = 1015777. Its totient is φ = 163840.

The previous prime is 409597. The next prime is 409609. The reversal of 409600 is 6904.

It is a happy number.

The square root of 409600 is 640.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 147456 + 262144 = 384^2 + 512^2 .

It is a Duffinian number.

It is a plaindrome in base 13.

It is a nialpdrome in base 16.

It is not an unprimeable number, because it can be changed into a prime (409609) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 81918 + ... + 81922.

2⁴⁰⁹⁶⁰⁰ is an apocalyptic number.

409600 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

409600 is the 640-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 409600

409600 is an abundant number, since it is smaller than the sum of its proper divisors (606177).

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

409600 is an frugal number, since it uses more digits than its factorization.

409600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 38 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 216, while the sum is 19.

The cubic root of 409600 is about 74.2654213378.

The spelling of 409600 in words is "four hundred nine thousand, six hundred".