413357824 has 72 divisors (see below), whose sum is σ = 905451120. Its totient is φ = 186777600.

The previous prime is 413357803. The next prime is 413357827. The reversal of 413357824 is 428753314.

It is a happy number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413357827) 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 7 ways as a sum of consecutive naturals, for example, 644544 + ... + 645184.

It is an arithmetic number, because the mean of its divisors is an integer number (12575710).

Almost surely, 2^413357824 is an apocalyptic number.

413357824 is a gapful number since it is divisible by the number (44) 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 413357824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (452725560).

413357824 is an abundant number, since it is smaller than the sum of its proper divisors (492093296).

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

413357824 is a wasteful number, since it uses less digits than its factorization.

413357824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 897 (or 883 counting only the distinct ones).

The product of its digits is 80640, while the sum is 37.

The square root of 413357824 is about 20331.2032108284. The cubic root of 413357824 is about 744.9184325814.

The spelling of 413357824 in words is "four hundred thirteen million, three hundred fifty-seven thousand, eight hundred twenty-four".