409131600 has 120 divisors (see below), whose sum is σ = 1315570560. Its totient is φ = 108687360.

The previous prime is 409131587. The next prime is 409131647. The reversal of 409131600 is 6131904.

It is a tau number, because it is divible by the number of its divisors (120).

It is a super-2 number, since 2×409131600² = 334777332237120000, which contains 22 as substring.

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.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 439936 + ... + 440864.

It is an arithmetic number, because the mean of its divisors is an integer number (10963088).

Almost surely, 2^409131600 is an apocalyptic number.

409131600 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 409131600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (657785280).

409131600 is an abundant number, since it is smaller than the sum of its proper divisors (906438960).

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

409131600 is a wasteful number, since it uses less digits than its factorization.

409131600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1317 (or 1306 counting only the distinct ones).

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

The square root of 409131600 is about 20227.0017550798. The cubic root of 409131600 is about 742.3710168314.

The spelling of 409131600 in words is "four hundred nine million, one hundred thirty-one thousand, six hundred".