82112400 has 120 divisors (see below), whose sum is σ = 292297760. Its totient is φ = 21893760.

The previous prime is 82112399. The next prime is 82112411. The reversal of 82112400 is 421128.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 6999 + ... + 14601.

Almost surely, 2^82112400 is an apocalyptic number.

82112400 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 82112400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146148880).

82112400 is an abundant number, since it is smaller than the sum of its proper divisors (210185360).

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

82112400 is a wasteful number, since it uses less digits than its factorization.

82112400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7630 (or 7613 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 18.

The square root of 82112400 is about 9061.5892645827. The cubic root of 82112400 is about 434.6465618981.

Adding to 82112400 its reverse (421128), we get a palindrome (82533528).

The spelling of 82112400 in words is "eighty-two million, one hundred twelve thousand, four hundred".