825120864 has 96 divisors (see below), whose sum is σ = 2419200000. Its totient is φ = 273601152.

The previous prime is 825120853. The next prime is 825120889. The reversal of 825120864 is 468021528.

825120864 is a `hidden beast` number, since 82 + 512 + 0 + 8 + 64 = 666.

It is a tau number, because it is divible by the number of its divisors (96).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 169537 + ... + 174335.

It is an arithmetic number, because the mean of its divisors is an integer number (25200000).

Almost surely, 2^825120864 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 825120864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1209600000).

825120864 is an abundant number, since it is smaller than the sum of its proper divisors (1594079136).

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

825120864 is a wasteful number, since it uses less digits than its factorization.

825120864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5017 (or 5003 counting only the distinct ones).

The product of its (nonzero) digits is 30720, while the sum is 36.

The square root of 825120864 is about 28724.9171278178. The cubic root of 825120864 is about 937.9345262483.

The spelling of 825120864 in words is "eight hundred twenty-five million, one hundred twenty thousand, eight hundred sixty-four".