85170380288400 has 2025 divisors, whose sum is σ = 346156201097553. Its totient is φ = 20040480345600.

The previous prime is 85170380288297. The next prime is 85170380288431. The reversal of 85170380288400 is 488208307158.

The square root of 85170380288400 is 9228780.

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

85170380288400 is a `hidden beast` number, since 8 + 517 + 0 + 3 + 8 + 0 + 2 + 88 + 40 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 30661336903824 + 54509043384576 = 5537268^2 + 7383024^2 .

It is a tau number, because it is divible by the number of its divisors (2025).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 404 ways as a sum of consecutive naturals, for example, 1078106079561 + ... + 1078106079639.

Almost surely, 2^{85170380288400} is an apocalyptic number.

85170380288400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

85170380288400 is the 9228780-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 85170380288400

85170380288400 is an abundant number, since it is smaller than the sum of its proper divisors (260985820809153).

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

85170380288400 is a wasteful number, since it uses less digits than its factorization.

85170380288400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 328 (or 159 counting only the distinct ones).

The product of its (nonzero) digits is 3440640, while the sum is 54.

The spelling of 85170380288400 in words is "eighty-five trillion, one hundred seventy billion, three hundred eighty million, two hundred eighty-eight thousand, four hundred".