413457824 has 48 divisors (see below), whose sum is σ = 881947080. Its totient is φ = 190794240.

The previous prime is 413457791. The next prime is 413457839. The reversal of 413457824 is 428754314.

It can be written as a sum of positive squares in 4 ways, for example, as 57456400 + 356001424 = 7580^2 + 18868^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 67364 + ... + 73244.

Almost surely, 2^413457824 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 413457824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (440973540).

413457824 is an abundant number, since it is smaller than the sum of its proper divisors (468489256).

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

413457824 is an equidigital number, since it uses as much as digits as its factorization.

413457824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5930 (or 5896 counting only the distinct ones).

The product of its digits is 107520, while the sum is 38.

The square root of 413457824 is about 20333.6623361361. The cubic root of 413457824 is about 744.9784982459.

The spelling of 413457824 in words is "four hundred thirteen million, four hundred fifty-seven thousand, eight hundred twenty-four".