413328 has 40 divisors (see below), whose sum is σ = 1091200. Its totient is φ = 134784.

The previous prime is 413299. The next prime is 413353. The reversal of 413328 is 823314.

It is a happy number.

It is a nude number because it is divisible by every one of its digits.

It is an unprimeable number.

413328 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 3738 + ... + 3846.

It is an arithmetic number, because the mean of its divisors is an integer number (27280).

2⁴¹³³²⁸ is an apocalyptic number.

413328 is a gapful number since it is divisible by the number (48) 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 413328, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (545600).

413328 is an abundant number, since it is smaller than the sum of its proper divisors (677872).

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

413328 is a wasteful number, since it uses less digits than its factorization.

413328 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 199 (or 193 counting only the distinct ones).

The product of its digits is 576, while the sum is 21.

The square root of 413328 is about 642.9059029127. The cubic root of 413328 is about 74.4900516722.

It can be divided in two parts, 413 and 328, that added together give a triangular number (741 = T₃₈).

The spelling of 413328 in words is "four hundred thirteen thousand, three hundred twenty-eight".