82919600240400 has 3645 divisors, whose sum is σ = 387368305339743. Its totient is φ = 16994018764800.

The previous prime is 82919600240371. The next prime is 82919600240459. The reversal of 82919600240400 is 404200691928.

The square root of 82919600240400 is 9106020.

It is a perfect power (a square), and thus also a powerful number.

82919600240400 is a `hidden beast` number, since 8 + 2 + 9 + 19 + 600 + 24 + 0 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 453731571216 + 82465868669184 = 673596^2 + 9081072^2 .

It is a tau number, because it is divible by the number of its divisors (3645).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 728 ways as a sum of consecutive naturals, for example, 1135884934764 + ... + 1135884934836.

Almost surely, 2^{82919600240400} is an apocalyptic number.

82919600240400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

82919600240400 is the 9106020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82919600240400

82919600240400 is an abundant number, since it is smaller than the sum of its proper divisors (304448705099343).

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

82919600240400 is an equidigital number, since it uses as much as digits as its factorization.

82919600240400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 224 (or 101 counting only the distinct ones).

The product of its (nonzero) digits is 248832, while the sum is 45.

The spelling of 82919600240400 in words is "eighty-two trillion, nine hundred nineteen billion, six hundred million, two hundred forty thousand, four hundred".