82771600 has 60 divisors (see below), whose sum is σ = 209344240. Its totient is φ = 31363200.

The previous prime is 82771583. The next prime is 82771607. The reversal of 82771600 is 617728.

It is a happy number.

It is a super-2 number, since 2×82771600² = 13702275533120000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (82771607) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2155 + ... + 13045.

Almost surely, 2^82771600 is an apocalyptic number.

82771600 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 82771600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (104672120).

82771600 is an abundant number, since it is smaller than the sum of its proper divisors (126572640).

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

82771600 is a wasteful number, since it uses less digits than its factorization.

82771600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 10928 (or 10917 counting only the distinct ones).

The product of its (nonzero) digits is 4704, while the sum is 31.

The square root of 82771600 is about 9097.8898652380. The cubic root of 82771600 is about 435.8065803128.

It can be divided in two parts, 827 and 71600, that added together give a palindrome (72427).

The spelling of 82771600 in words is "eighty-two million, seven hundred seventy-one thousand, six hundred".