85188096900 has 567 divisors, whose sum is σ = 296030586901. Its totient is φ = 21266815680.

The previous prime is 85188096883. The next prime is 85188096913. The reversal of 85188096900 is 969088158.

The square root of 85188096900 is 291870.

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

It can be written as a sum of positive squares in only one way, i.e., 30667714884 + 54520382016 = 175122^2 + 233496^2 .

It is a super-2 number, since 2×85188096900² (a number of 23 digits) contains 22 as substring.

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

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 188 ways as a sum of consecutive naturals, for example, 1812512677 + ... + 1812512723.

Almost surely, 2^85188096900 is an apocalyptic number.

85188096900 is the 291870-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 85188096900

85188096900 is an abundant number, since it is smaller than the sum of its proper divisors (210842490001).

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

85188096900 is a wasteful number, since it uses less digits than its factorization.

85188096900 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 172 (or 80 counting only the distinct ones).

The product of its (nonzero) digits is 1244160, while the sum is 54.

The spelling of 85188096900 in words is "eighty-five billion, one hundred eighty-eight million, ninety-six thousand, nine hundred".