463584 has 48 divisors (see below), whose sum is σ = 1330560. Its totient is φ = 140160.

The previous prime is 463579. The next prime is 463613. The reversal of 463584 is 485364.

It is a tau number, because it is divible by the number of its divisors (48).

It is a d-powerful number, because it can be written as 4⁷ + 6⁵ + 5³ + 3¹¹ + 8 + 4⁹ .

It is a congruent number.

It is an unprimeable number.

463584 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, 837 + ... + 1275.

It is an arithmetic number, because the mean of its divisors is an integer number (27720).

2⁴⁶³⁵⁸⁴ is an apocalyptic number.

463584 is a gapful number since it is divisible by the number (44) 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 463584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (665280).

463584 is an abundant number, since it is smaller than the sum of its proper divisors (866976).

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

463584 is a wasteful number, since it uses less digits than its factorization.

463584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 463 (or 455 counting only the distinct ones).

The product of its digits is 11520, while the sum is 30.

The square root of 463584 is about 680.8700316507. The cubic root of 463584 is about 77.3943896206.

The spelling of 463584 in words is "four hundred sixty-three thousand, five hundred eighty-four".