821400 has 72 divisors (see below), whose sum is σ = 2617020. Its totient is φ = 213120.

The previous prime is 821383. The next prime is 821411. The reversal of 821400 is 4128.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 821400.

It is a congruent number.

It is an unprimeable number.

821400 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 17 ways as a sum of consecutive naturals, for example, 22182 + ... + 22218.

2⁸²¹⁴⁰⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 821400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1308510).

821400 is an abundant number, since it is smaller than the sum of its proper divisors (1795620).

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

821400 is a wasteful number, since it uses less digits than its factorization.

821400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 93 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 15.

The square root of 821400 is about 906.3112048298. The cubic root of 821400 is about 93.6522536780.

Adding to 821400 its reverse (4128), we get a palindrome (825528).

It can be divided in two parts, 821 and 400, that added together give a palindrome (1221).

The spelling of 821400 in words is "eight hundred twenty-one thousand, four hundred".