413400000 has 336 divisors, whose sum is σ = 1500091488. Its totient is φ = 99840000.

The previous prime is 413399993. The next prime is 413400011. The reversal of 413400000 is 4314.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 7799974 + ... + 7800026.

It is an arithmetic number, because the mean of its divisors is an integer number (4464558).

Almost surely, 2^413400000 is an apocalyptic number.

413400000 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 413400000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (750045744).

413400000 is an abundant number, since it is smaller than the sum of its proper divisors (1086691488).

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

413400000 is an equidigital number, since it uses as much as digits as its factorization.

413400000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 106 (or 76 counting only the distinct ones).

The product of its (nonzero) digits is 48, while the sum is 12.

The square root of 413400000 is about 20332.2404077859. The cubic root of 413400000 is about 744.9437670572.

Adding to 413400000 its reverse (4314), we get a palindrome (413404314).

The spelling of 413400000 in words is "four hundred thirteen million, four hundred thousand".