82551600 has 180 divisors, whose sum is σ = 299232336. Its totient is φ = 21035520.

The previous prime is 82551593. The next prime is 82551617. The reversal of 82551600 is 615528.

82551600 is a `hidden beast` number, since 8 + 2 + 5 + 51 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (180).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 82302 + ... + 83298.

Almost surely, 2^82551600 is an apocalyptic number.

82551600 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 82551600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149616168).

82551600 is an abundant number, since it is smaller than the sum of its proper divisors (216680736).

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

82551600 is a wasteful number, since it uses less digits than its factorization.

82551600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1044 (or 1030 counting only the distinct ones).

The product of its (nonzero) digits is 2400, while the sum is 27.

The square root of 82551600 is about 9085.7911047965. The cubic root of 82551600 is about 435.4201252240.

It can be divided in two parts, 825 and 51600, that added together give a palindrome (52425).

The spelling of 82551600 in words is "eighty-two million, five hundred fifty-one thousand, six hundred".