820034800 has 120 divisors (see below), whose sum is σ = 2135957040. Its totient is φ = 300748800.

The previous prime is 820034783. The next prime is 820034807. The reversal of 820034800 is 8430028.

It is a super-2 number, since 2×820034800² = 1344914146422080000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (820034807) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 930360 + ... + 931240.

It is an arithmetic number, because the mean of its divisors is an integer number (17799642).

Almost surely, 2^820034800 is an apocalyptic number.

820034800 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 820034800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1067978520).

820034800 is an abundant number, since it is smaller than the sum of its proper divisors (1315922240).

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

820034800 is a wasteful number, since it uses less digits than its factorization.

820034800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1091 (or 1080 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 25.

The square root of 820034800 is about 28636.2497544633. The cubic root of 820034800 is about 936.0034029633.

Adding to 820034800 its reverse (8430028), we get a palindrome (828464828).

The spelling of 820034800 in words is "eight hundred twenty million, thirty-four thousand, eight hundred".