821600 has 72 divisors (see below), whose sum is σ = 2187360. Its totient is φ = 299520.

The previous prime is 821573. The next prime is 821603. The reversal of 821600 is 6128.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (821603) by changing a digit.

821600 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 11 ways as a sum of consecutive naturals, for example, 10361 + ... + 10439.

It is an arithmetic number, because the mean of its divisors is an integer number (30380).

2⁸²¹⁶⁰⁰ is an apocalyptic number.

821600 is a gapful number since it is divisible by the number (80) 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 821600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1093680).

821600 is an abundant number, since it is smaller than the sum of its proper divisors (1365760).

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

821600 is a wasteful number, since it uses less digits than its factorization.

821600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 112 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 17.

The square root of 821600 is about 906.4215354900. The cubic root of 821600 is about 93.6598540881.

Adding to 821600 its reverse (6128), we get a palindrome (827728).

The spelling of 821600 in words is "eight hundred twenty-one thousand, six hundred".