826394400 has 504 divisors, whose sum is σ = 3287328660. Its totient is φ = 201553920.

The previous prime is 826394351. The next prime is 826394501. The reversal of 826394400 is 4493628.

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 225360144 + 601034256 = 15012^2 + 24516^2 .

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

It is an unprimeable number.

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 83 ways as a sum of consecutive naturals, for example, 7581546 + ... + 7581654.

Almost surely, 2^826394400 is an apocalyptic number.

826394400 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 826394400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1643664330).

826394400 is an abundant number, since it is smaller than the sum of its proper divisors (2460934260).

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

826394400 is a wasteful number, since it uses less digits than its factorization.

826394400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 160 (or 132 counting only the distinct ones).

The product of its (nonzero) digits is 41472, while the sum is 36.

The square root of 826394400 is about 28747.0763730853. The cubic root of 826394400 is about 938.4168310899.

The spelling of 826394400 in words is "eight hundred twenty-six million, three hundred ninety-four thousand, four hundred".