409041600 has 336 divisors, whose sum is σ = 1499713536. Its totient is φ = 96768000.

The previous prime is 409041599. The next prime is 409041601. The reversal of 409041600 is 6140904.

It is an interprime number because it is at equal distance from previous prime (409041599) and next prime (409041601).

It is a super-3 number, since 3×409041600³ (a number of 27 digits) contains 333 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (409041601) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3220737 + ... + 3220863.

Almost surely, 2^409041600 is an apocalyptic number.

409041600 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 409041600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (749856768).

409041600 is an abundant number, since it is smaller than the sum of its proper divisors (1090671936).

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

409041600 is a wasteful number, since it uses less digits than its factorization.

409041600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 224 (or 209 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 24.

The square root of 409041600 is about 20224.7768838126. The cubic root of 409041600 is about 742.3165777126.

The spelling of 409041600 in words is "four hundred nine million, forty-one thousand, six hundred".