827020800 has 240 divisors, whose sum is σ = 3036836880. Its totient is φ = 220446720.

The previous prime is 827020769. The next prime is 827020801. The reversal of 827020800 is 8020728.

It is a tau number, because it is divible by the number of its divisors (240).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (827020801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 344404 + ... + 346796.

It is an arithmetic number, because the mean of its divisors is an integer number (12653487).

Almost surely, 2^827020800 is an apocalyptic number.

827020800 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 827020800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1518418440).

827020800 is an abundant number, since it is smaller than the sum of its proper divisors (2209816080).

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

827020800 is a wasteful number, since it uses less digits than its factorization.

827020800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2430 (or 2403 counting only the distinct ones).

The product of its (nonzero) digits is 1792, while the sum is 27.

The square root of 827020800 is about 28757.9693302570. The cubic root of 827020800 is about 938.6538752274.

The spelling of 827020800 in words is "eight hundred twenty-seven million, twenty thousand, eight hundred".