413505600 has 168 divisors, whose sum is σ = 1365918528. Its totient is φ = 109516800.

The previous prime is 413505563. The next prime is 413505601. The reversal of 413505600 is 6505314.

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 (413505601) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1329445 + ... + 1329755.

Almost surely, 2^413505600 is an apocalyptic number.

413505600 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 413505600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (682959264).

413505600 is an abundant number, since it is smaller than the sum of its proper divisors (952412928).

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

413505600 is a wasteful number, since it uses less digits than its factorization.

413505600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 613 (or 598 counting only the distinct ones).

The product of its (nonzero) digits is 1800, while the sum is 24.

The square root of 413505600 is about 20334.8371028636. The cubic root of 413505600 is about 745.0071917988.

The spelling of 413505600 in words is "four hundred thirteen million, five hundred five thousand, six hundred".