826610400 has 864 divisors, whose sum is σ = 3847253760. Its totient is φ = 169344000.

The previous prime is 826610399. The next prime is 826610413. The reversal of 826610400 is 4016628.

826610400 is a `hidden beast` number, since 8 + 2 + 6 + 610 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (864).

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 a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

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 143 ways as a sum of consecutive naturals, for example, 11642365 + ... + 11642435.

It is an arithmetic number, because the mean of its divisors is an integer number (4452840).

Almost surely, 2^826610400 is an apocalyptic number.

826610400 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 826610400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1923626880).

826610400 is an abundant number, since it is smaller than the sum of its proper divisors (3020643360).

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

826610400 is a wasteful number, since it uses less digits than its factorization.

826610400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 125 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 826610400 is about 28750.8330314097. The cubic root of 826610400 is about 938.4985839744.

The spelling of 826610400 in words is "eight hundred twenty-six million, six hundred ten thousand, four hundred".