82736769600 has 945 divisors, whose sum is σ = 330081146923. Its totient is φ = 20323491840.

The previous prime is 82736769589. The next prime is 82736769607. The reversal of 82736769600 is 696763728.

The square root of 82736769600 is 287640.

It is a perfect power (a square), and thus also a powerful number.

82736769600 is a `hidden beast` number, since 8 + 27 + 3 + 6 + 7 + 6 + 9 + 600 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 1935296064 + 80801473536 = 43992^2 + 284256^2 .

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (82736769607) by changing a digit.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 1760356777 + ... + 1760356823.

Almost surely, 2^82736769600 is an apocalyptic number.

82736769600 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

82736769600 is the 287640-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82736769600

82736769600 is an abundant number, since it is smaller than the sum of its proper divisors (247344377323).

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

82736769600 is a wasteful number, since it uses less digits than its factorization.

82736769600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 162 (or 74 counting only the distinct ones).

The product of its (nonzero) digits is 4572288, while the sum is 54.

The spelling of 82736769600 in words is "eighty-two billion, seven hundred thirty-six million, seven hundred sixty-nine thousand, six hundred".