413509824 has 420 divisors, whose sum is σ = 1553815536. Its totient is φ = 104315904.

The previous prime is 413509813. The next prime is 413509829. The reversal of 413509824 is 428905314.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413509829) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 17978677 + ... + 17978699.

Almost surely, 2^413509824 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 413509824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (776907768).

413509824 is an abundant number, since it is smaller than the sum of its proper divisors (1140305712).

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

413509824 is a wasteful number, since it uses less digits than its factorization.

413509824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 82 (or 48 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The square root of 413509824 is about 20334.9409637697. The cubic root of 413509824 is about 745.0097285639.

The spelling of 413509824 in words is "four hundred thirteen million, five hundred nine thousand, eight hundred twenty-four".