61824 has 64 divisors (see below), whose sum is σ = 195840. Its totient is φ = 16896.

The previous prime is 61819. The next prime is 61837. The reversal of 61824 is 42816.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is one of the 548 Lynch-Bell numbers.

It is a zygodrome in base 2.

It is a self number, because there is not a number n which added to its sum of digits gives 61824.

It is a congruent number.

It is an unprimeable number.

61824 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, 2677 + ... + 2699.

It is an arithmetic number, because the mean of its divisors is an integer number (3060).

2⁶¹⁸²⁴ is an apocalyptic number.

61824 is a gapful number since it is divisible by the number (64) 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 61824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (97920).

61824 is an abundant number, since it is smaller than the sum of its proper divisors (134016).

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

61824 is a wasteful number, since it uses less digits than its factorization.

61824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 47 (or 35 counting only the distinct ones).

The product of its digits is 384, while the sum is 21.

The square root of 61824 is about 248.6443242867. The cubic root of 61824 is about 39.5414295859.

61824 divided by its product of digits (384) gives a palindrome (161).

It can be divided in two parts, 6 and 1824, that added together give a triangular number (1830 = T₆₀).

The spelling of 61824 in words is "sixty-one thousand, eight hundred twenty-four".