413310000 has 200 divisors, whose sum is σ = 1394553600. Its totient is φ = 105248000.

The previous prime is 413309999. The next prime is 413310019. The reversal of 413310000 is 13314.

It is a tau number, because it is divible by the number of its divisors (200).

It is a super-2 number, since 2×413310000² = 341650312200000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is an unprimeable number.

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 39 ways as a sum of consecutive naturals, for example, 689701 + ... + 690299.

It is an arithmetic number, because the mean of its divisors is an integer number (6972768).

Almost surely, 2^413310000 is an apocalyptic number.

413310000 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 413310000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (697276800).

413310000 is an abundant number, since it is smaller than the sum of its proper divisors (981243600).

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

413310000 is a wasteful number, since it uses less digits than its factorization.

413310000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 653 (or 632 counting only the distinct ones).

The product of its (nonzero) digits is 36, while the sum is 12.

The square root of 413310000 is about 20330.0270535973. The cubic root of 413310000 is about 744.8897033538.

Adding to 413310000 its reverse (13314), we get a palindrome (413323314).

The spelling of 413310000 in words is "four hundred thirteen million, three hundred ten thousand".