825121440 has 288 divisors, whose sum is σ = 3308812416. Its totient is φ = 184596480.

The previous prime is 825121439. The next prime is 825121457. The reversal of 825121440 is 44121528.

825121440 is a `hidden beast` number, since 8 + 2 + 512 + 144 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

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 an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 203917 + ... + 207923.

It is an arithmetic number, because the mean of its divisors is an integer number (11488932).

Almost surely, 2^825121440 is an apocalyptic number.

825121440 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 825121440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1654406208).

825121440 is an abundant number, since it is smaller than the sum of its proper divisors (2483690976).

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

825121440 is a wasteful number, since it uses less digits than its factorization.

825121440 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4052 (or 4041 counting only the distinct ones).

The product of its (nonzero) digits is 2560, while the sum is 27.

The square root of 825121440 is about 28724.9271539546. The cubic root of 825121440 is about 937.9347444992.

Adding to 825121440 its reverse (44121528), we get a palindrome (869242968).

It can be divided in two parts, 825 and 121440, that added together give a triangular number (122265 = T₄₉₄).

The spelling of 825121440 in words is "eight hundred twenty-five million, one hundred twenty-one thousand, four hundred forty".