825350400 has 648 divisors, whose sum is σ = 3558522240. Its totient is φ = 178421760.

The previous prime is 825350389. The next prime is 825350401. The reversal of 825350400 is 4053528.

825350400 is a `hidden beast` number, since 8 + 253 + 5 + 0 + 400 = 666.

It is not an unprimeable number, because it can be changed into a prime (825350401) 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 71 ways as a sum of consecutive naturals, for example, 9273556 + ... + 9273644.

Almost surely, 2^825350400 is an apocalyptic number.

825350400 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 825350400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1779261120).

825350400 is an abundant number, since it is smaller than the sum of its proper divisors (2733171840).

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

825350400 is a wasteful number, since it uses less digits than its factorization.

825350400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 151 (or 129 counting only the distinct ones).

The product of its (nonzero) digits is 4800, while the sum is 27.

The square root of 825350400 is about 28728.9122662171. The cubic root of 825350400 is about 938.0214911963.

It can be divided in two parts, 8253 and 50400, that added together give a triangular number (58653 = T₃₄₂).

The spelling of 825350400 in words is "eight hundred twenty-five million, three hundred fifty thousand, four hundred".