413984 has 24 divisors (see below), whose sum is σ = 864108. Its totient is φ = 194560.

The previous prime is 413981. The next prime is 414013. The reversal of 413984 is 489314.

It can be written as a sum of positive squares in 2 ways, for example, as 394384 + 19600 = 628^2 + 140^2 .

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 413984.

It is not an unprimeable number, because it can be changed into a prime (413981) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 164 + ... + 924.

2⁴¹³⁹⁸⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (432054).

413984 is an abundant number, since it is smaller than the sum of its proper divisors (450124).

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

413984 is a wasteful number, since it uses less digits than its factorization.

413984 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 788 (or 780 counting only the distinct ones).

The product of its digits is 3456, while the sum is 29.

The square root of 413984 is about 643.4158841682. The cubic root of 413984 is about 74.5294389909.

The spelling of 413984 in words is "four hundred thirteen thousand, nine hundred eighty-four".