462624 has 48 divisors (see below), whose sum is σ = 1249920. Its totient is φ = 149760.

The previous prime is 462607. The next prime is 462629. The reversal of 462624 is 426264.

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

It is a Harshad number since it is a multiple of its sum of digits (24).

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

It is a junction number, because it is equal to n+sod(n) for n = 462594 and 462603.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (462629) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 5817 + ... + 5895.

It is an arithmetic number, because the mean of its divisors is an integer number (26040).

2⁴⁶²⁶²⁴ 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 462624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (624960).

462624 is an abundant number, since it is smaller than the sum of its proper divisors (787296).

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

462624 is a wasteful number, since it uses less digits than its factorization.

462624 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 153 (or 145 counting only the distinct ones).

The product of its digits is 2304, while the sum is 24.

The square root of 462624 is about 680.1646859401. The cubic root of 462624 is about 77.3409293635.

Subtracting from 462624 its product of digits (2304), we obtain a triangular number (460320 = T₉₅₉).

Adding to 462624 its reverse (426264), we get a palindrome (888888).

The spelling of 462624 in words is "four hundred sixty-two thousand, six hundred twenty-four".