825309574128 has 960 divisors, whose sum is σ = 2828098990080. Its totient is φ = 230965862400.

The previous prime is 825309574027. The next prime is 825309574147. The reversal of 825309574128 is 821475903528.

825309574128 is a `hidden beast` number, since 8 + 2 + 53 + 0 + 9 + 574 + 12 + 8 = 666.

It is a super-2 number, since 2×825309574128² (a number of 25 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 1863001075 + ... + 1863001517.

It is an arithmetic number, because the mean of its divisors is an integer number (2945936448).

Almost surely, 2^825309574128 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 825309574128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1414049495040).

825309574128 is an abundant number, since it is smaller than the sum of its proper divisors (2002789415952).

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

825309574128 is a wasteful number, since it uses less digits than its factorization.

825309574128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 580 (or 562 counting only the distinct ones).

The product of its (nonzero) digits is 4838400, while the sum is 54.

The spelling of 825309574128 in words is "eight hundred twenty-five billion, three hundred nine million, five hundred seventy-four thousand, one hundred twenty-eight".