• Deleting all the even digits from 2^{824} we obtain a prime of 133 digits.

824 has 8 divisors (see below), whose sum is σ = 1560. Its totient is φ = 408.

The previous prime is 823. The next prime is 827. The reversal of 824 is 428.

824 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (8).

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

It is one of the 548 Lynch-Bell numbers.

824 is a modest number, since divided by 24 gives 8 as remainder.

It is a plaindrome in base 5, base 7, base 9, base 11, base 12, base 15 and base 16.

It is a zygodrome in base 2 and base 7.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 799 and 808.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (821) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 44 + ... + 59.

It is an arithmetic number, because the mean of its divisors is an integer number (195).

2^{824} is an apocalyptic number.

It is an amenable number.

824 is a deficient number, since it is larger than the sum of its proper divisors (736).

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

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

The sum of its prime factors is 109 (or 105 counting only the distinct ones).

The product of its digits is 64, while the sum is 14.

The square root of 824 is about 28.7054001888. The cubic root of 824 is about 9.3750962953.

Adding to 824 its sum of digits (14), we get a palindrome (838).

Adding to 824 its product of digits (64), we get a palindrome (888).

It can be divided in two parts, 8 and 24, that added together give a 5-th power (32 = 2^{5}).

The spelling of 824 in words is "eight hundred twenty-four", and thus it is an aban number.

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