82195766400 has 768 divisors, whose sum is σ = 307695484800. Its totient is φ = 19110297600.

The previous prime is 82195766399. The next prime is 82195766407. The reversal of 82195766400 is 466759128.

It is a super-2 number, since 2×82195766400² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 82195766400.

It is not an unprimeable number, because it can be changed into a prime (82195766407) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 425884704 + ... + 425884896.

Almost surely, 2^82195766400 is an apocalyptic number.

82195766400 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 82195766400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (153847742400).

82195766400 is an abundant number, since it is smaller than the sum of its proper divisors (225499718400).

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

82195766400 is a wasteful number, since it uses less digits than its factorization.

82195766400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 377 (or 360 counting only the distinct ones).

The product of its (nonzero) digits is 725760, while the sum is 48.

The spelling of 82195766400 in words is "eighty-two billion, one hundred ninety-five million, seven hundred sixty-six thousand, four hundred".