81782434339200 has 960 divisors, whose sum is σ = 356035096581120. Its totient is φ = 18090111283200.

The previous prime is 81782434339187. The next prime is 81782434339279. The reversal of 81782434339200 is 293343428718.

It is a happy number.

81782434339200 is a `hidden beast` number, since 8 + 1 + 7 + 8 + 243 + 4 + 3 + 392 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 55519399 + ... + 56973401.

It is an arithmetic number, because the mean of its divisors is an integer number (370869892272).

Almost surely, 2^{81782434339200} is an apocalyptic number.

81782434339200 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 81782434339200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (178017548290560).

81782434339200 is an abundant number, since it is smaller than the sum of its proper divisors (274252662241920).

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

81782434339200 is a wasteful number, since it uses less digits than its factorization.

81782434339200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1454077 (or 1454051 counting only the distinct ones).

The product of its (nonzero) digits is 6967296, while the sum is 54.

The spelling of 81782434339200 in words is "eighty-one trillion, seven hundred eighty-two billion, four hundred thirty-four million, three hundred thirty-nine thousand, two hundred".