51624 has 32 divisors (see below), whose sum is σ = 144000. Its totient is φ = 17136.

The previous prime is 51613. The next prime is 51631. The reversal of 51624 is 42615.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 9.

It is a junction number, because it is equal to n+sod(n) for n = 51597 and 51606.

It is a congruent number.

It is an unprimeable number.

51624 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 7 ways as a sum of consecutive naturals, for example, 97 + ... + 335.

It is an arithmetic number, because the mean of its divisors is an integer number (4500).

2⁵¹⁶²⁴ is an apocalyptic number.

51624 is a gapful number since it is divisible by the number (54) formed by its first and last digit.

51624 is the 144-th heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 51624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (72000).

51624 is an abundant number, since it is smaller than the sum of its proper divisors (92376).

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

51624 is a wasteful number, since it uses less digits than its factorization.

51624 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 254 (or 244 counting only the distinct ones).

The product of its digits is 240, while the sum is 18.

The square root of 51624 is about 227.2091547451. The cubic root of 51624 is about 37.2349307694.

Subtracting from 51624 its reverse (42615), we obtain a palindrome (9009).

The spelling of 51624 in words is "fifty-one thousand, six hundred twenty-four".