820800 has 168 divisors, whose sum is σ = 3149600. Its totient is φ = 207360.

The previous prime is 820793. The next prime is 820837. The reversal of 820800 is 8028.

Added to its reverse (8028) it gives a triangular number (828828 = T₁₂₈₇).

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

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 16.

It is a zygodrome in base 15.

It is an unprimeable number.

820800 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 23 ways as a sum of consecutive naturals, for example, 43191 + ... + 43209.

2⁸²⁰⁸⁰⁰ is an apocalyptic number.

820800 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 820800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1574800).

820800 is an abundant number, since it is smaller than the sum of its proper divisors (2328800).

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

820800 is a wasteful number, since it uses less digits than its factorization.

820800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 50 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 18.

The square root of 820800 is about 905.9801322325. The cubic root of 820800 is about 93.6294450425.

Adding to 820800 its reverse (8028), we get a palindrome (828828).

The spelling of 820800 in words is "eight hundred twenty thousand, eight hundred".