465984 has 42 divisors (see below), whose sum is σ = 1337310. Its totient is φ = 155136.

The previous prime is 465977. The next prime is 465989. The reversal of 465984 is 489564.

It can be written as a sum of positive squares in only one way, i.e., 451584 + 14400 = 672^2 + 120^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (465989) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 172 + ... + 980.

465984 is a Friedman number, since it can be written as 4854*96, using all its digits and the basic arithmetic operations.

2⁴⁶⁵⁹⁸⁴ 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 465984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (668655).

465984 is an abundant number, since it is smaller than the sum of its proper divisors (871326).

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

465984 is a wasteful number, since it uses less digits than its factorization.

465984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 827 (or 814 counting only the distinct ones).

The product of its digits is 34560, while the sum is 36.

The square root of 465984 is about 682.6302073597. The cubic root of 465984 is about 77.5277181464.

The spelling of 465984 in words is "four hundred sixty-five thousand, nine hundred eighty-four".