821146982400 has 1152 divisors, whose sum is σ = 3126299904000. Its totient is φ = 211168788480.

The previous prime is 821146982363. The next prime is 821146982429. The reversal of 821146982400 is 4289641128.

821146982400 is a `hidden beast` number, since 8 + 21 + 146 + 9 + 82 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

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 95 ways as a sum of consecutive naturals, for example, 7972300749 + ... + 7972300851.

It is an arithmetic number, because the mean of its divisors is an integer number (2713802000).

Almost surely, 2^821146982400 is an apocalyptic number.

821146982400 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 821146982400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1563149952000).

821146982400 is an abundant number, since it is smaller than the sum of its proper divisors (2305152921600).

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

821146982400 is a wasteful number, since it uses less digits than its factorization.

821146982400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 296 (or 265 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 45.

The spelling of 821146982400 in words is "eight hundred twenty-one billion, one hundred forty-six million, nine hundred eighty-two thousand, four hundred".