82819598400 has 1008 divisors, whose sum is σ = 370802659968. Its totient is φ = 17031168000.

The previous prime is 82819598387. The next prime is 82819598401. The reversal of 82819598400 is 489591828.

82819598400 is a `hidden beast` number, since 8 + 2 + 8 + 1 + 9 + 598 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1008).

It is not an unprimeable number, because it can be changed into a prime (82819598401) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 125294070 + ... + 125294730.

Almost surely, 2^82819598400 is an apocalyptic number.

82819598400 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 82819598400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (185401329984).

82819598400 is an abundant number, since it is smaller than the sum of its proper divisors (287983061568).

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

82819598400 is a wasteful number, since it uses less digits than its factorization.

82819598400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 820 (or 802 counting only the distinct ones).

The product of its (nonzero) digits is 1658880, while the sum is 54.

The spelling of 82819598400 in words is "eighty-two billion, eight hundred nineteen million, five hundred ninety-eight thousand, four hundred".