82761600 has 192 divisors, whose sum is σ = 281165040. Its totient is φ = 21381120.

The previous prime is 82761589. The next prime is 82761607. The reversal of 82761600 is 616728.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (192).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82761607) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 355084 + ... + 355316.

Almost surely, 2^82761600 is an apocalyptic number.

82761600 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 82761600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (140582520).

82761600 is an abundant number, since it is smaller than the sum of its proper divisors (198403440).

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

82761600 is a wasteful number, since it uses less digits than its factorization.

82761600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 297 (or 280 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 30.

The square root of 82761600 is about 9097.3402706505. The cubic root of 82761600 is about 435.7890290379.

The spelling of 82761600 in words is "eighty-two million, seven hundred sixty-one thousand, six hundred".