82952848742400 has 2304 divisors, whose sum is σ = 376825081651200. Its totient is φ = 17417762242560.

The previous prime is 82952848742359. The next prime is 82952848742437. The reversal of 82952848742400 is 424784825928.

82952848742400 is a `hidden beast` number, since 8 + 2 + 9 + 52 + 84 + 87 + 424 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2304).

It is a super-2 number, since 2×82952848742400² (a number of 29 digits) contains 22 as substring.

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 polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 28053041722 + ... + 28053044678.

It is an arithmetic number, because the mean of its divisors is an integer number (163552552800).

Almost surely, 2^{82952848742400} is an apocalyptic number.

82952848742400 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 82952848742400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (188412540825600).

82952848742400 is an abundant number, since it is smaller than the sum of its proper divisors (293872232908800).

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

82952848742400 is a wasteful number, since it uses less digits than its factorization.

82952848742400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3241 (or 3210 counting only the distinct ones).

The product of its (nonzero) digits is 82575360, while the sum is 63.

The spelling of 82952848742400 in words is "eighty-two trillion, nine hundred fifty-two billion, eight hundred forty-eight million, seven hundred forty-two thousand, four hundred".