103824 has 60 divisors (see below), whose sum is σ = 335296. Its totient is φ = 29376.

The previous prime is 103813. The next prime is 103837. The reversal of 103824 is 428301.

It is a happy number.

It is a Cunningham number, because it is equal to 47³+1.

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

It is a junction number, because it is equal to n+sod(n) for n = 103797 and 103806.

It is a congruent number.

It is an unprimeable 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 11 ways as a sum of consecutive naturals, for example, 957 + ... + 1059.

103824 is a Friedman number, since it can be written as (48-2^0)^3+1, using all its digits and the basic arithmetic operations.

2¹⁰³⁸²⁴ is an apocalyptic number.

103824 is a gapful number since it is divisible by the number (14) 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 103824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (167648).

103824 is an abundant number, since it is smaller than the sum of its proper divisors (231472).

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

103824 is a wasteful number, since it uses less digits than its factorization.

103824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 124 (or 115 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 103824 is about 322.2173179703. The cubic root of 103824 is about 47.0001508974. Note that the first 3 decimals are identical.

The spelling of 103824 in words is "one hundred three thousand, eight hundred twenty-four".