413000 has 64 divisors (see below), whose sum is σ = 1123200. Its totient is φ = 139200.

The previous prime is 412987. The next prime is 413009. The reversal of 413000 is 314.

It is a Harshad number since it is a multiple of its sum of digits (8).

It is a nialpdrome in base 14.

It is not an unprimeable number, because it can be changed into a prime (413009) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 6971 + ... + 7029.

It is an arithmetic number, because the mean of its divisors is an integer number (17550).

2⁴¹³⁰⁰⁰ is an apocalyptic number.

413000 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 413000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (561600).

413000 is an abundant number, since it is smaller than the sum of its proper divisors (710200).

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

413000 is a wasteful number, since it uses less digits than its factorization.

413000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 87 (or 73 counting only the distinct ones).

The product of its (nonzero) digits is 12, while the sum is 8.

The square root of 413000 is about 642.6507605224. The cubic root of 413000 is about 74.4703423835.

Adding to 413000 its reverse (314), we get a palindrome (413314).

Subtracting from 413000 its reverse (314), we obtain a triangular number (412686 = T₉₀₈).

The spelling of 413000 in words is "four hundred thirteen thousand".