82935014400 has 1056 divisors, whose sum is σ = 355034300160. Its totient is φ = 18579456000.

The previous prime is 82935014387. The next prime is 82935014401. The reversal of 82935014400 is 441053928.

82935014400 is a `hidden beast` number, since 82 + 93 + 50 + 1 + 440 + 0 = 666.

It is a super-3 number, since 3×82935014400³ (a number of 34 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82935014401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 295142260 + ... + 295142540.

Almost surely, 2^82935014400 is an apocalyptic number.

82935014400 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 82935014400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (177517150080).

82935014400 is an abundant number, since it is smaller than the sum of its proper divisors (272099285760).

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

82935014400 is a wasteful number, since it uses less digits than its factorization.

82935014400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 388 (or 359 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The spelling of 82935014400 in words is "eighty-two billion, nine hundred thirty-five million, fourteen thousand, four hundred".