826953471590400 has 7680 divisors, whose sum is σ = 4132260272701440. Its totient is φ = 158360666112000.

The previous prime is 826953471590399. The next prime is 826953471590413. The reversal of 826953471590400 is 4095174359628.

826953471590400 is a `hidden beast` number, since 8 + 2 + 6 + 9 + 5 + 34 + 7 + 1 + 590 + 4 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (7680).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 479 ways as a sum of consecutive naturals, for example, 3642966835087 + ... + 3642966835313.

It is an arithmetic number, because the mean of its divisors is an integer number (538054723008).

It is a 1-persistent number, because it is pandigital, but 2⋅826953471590400 = 1653906943180800 is not.

Almost surely, 2^{826953471590400} is an apocalyptic number.

826953471590400 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 826953471590400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2066130136350720).

826953471590400 is an abundant number, since it is smaller than the sum of its proper divisors (3305306801111040).

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

826953471590400 is a wasteful number, since it uses less digits than its factorization.

826953471590400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 351 (or 309 counting only the distinct ones).

The product of its (nonzero) digits is 65318400, while the sum is 63.

The spelling of 826953471590400 in words is "eight hundred twenty-six trillion, nine hundred fifty-three billion, four hundred seventy-one million, five hundred ninety thousand, four hundred".