825120878400 has 1512 divisors, whose sum is σ = 3834614818944. Its totient is φ = 166479667200.

The previous prime is 825120878381. The next prime is 825120878419. The reversal of 825120878400 is 4878021528.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (825120878381) and next prime (825120878419).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 210972445 + ... + 210976355.

It is an arithmetic number, because the mean of its divisors is an integer number (2536120912).

Almost surely, 2^825120878400 is an apocalyptic number.

825120878400 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 825120878400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1917307409472).

825120878400 is an abundant number, since it is smaller than the sum of its proper divisors (3009493940544).

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

825120878400 is a wasteful number, since it uses less digits than its factorization.

825120878400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3989 (or 3964 counting only the distinct ones).

The product of its (nonzero) digits is 286720, while the sum is 45.

Adding to 825120878400 its reverse (4878021528), we get a palindrome (829998899928).

The spelling of 825120878400 in words is "eight hundred twenty-five billion, one hundred twenty million, eight hundred seventy-eight thousand, four hundred".