82760400 has 240 divisors, whose sum is σ = 301369600. Its totient is φ = 21565440.

The previous prime is 82760399. The next prime is 82760407. The reversal of 82760400 is 406728.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82760407) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 853152 + ... + 853248.

Almost surely, 2^82760400 is an apocalyptic number.

82760400 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 82760400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (150684800).

82760400 is an abundant number, since it is smaller than the sum of its proper divisors (218609200).

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

82760400 is a wasteful number, since it uses less digits than its factorization.

82760400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 203 (or 186 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 82760400 is about 9097.2743170688. The cubic root of 82760400 is about 435.7869227899.

The spelling of 82760400 in words is "eighty-two million, seven hundred sixty thousand, four hundred".