8210116008900 has 1215 divisors, whose sum is σ = 30159992744343. Its totient is φ = 1931003193600.

The previous prime is 8210116008893. The next prime is 8210116008947. The reversal of 8210116008900 is 98006110128.

The square root of 8210116008900 is 2865330.

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

It can be written as a sum of positive squares in 4 ways, for example, as 2116169546436 + 6093946462464 = 1454706^2 + 2468592^2 .

It is a super-3 number, since 3×8210116008900³ (a number of 40 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

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, 103925519061 + ... + 103925519139.

Almost surely, 2^{8210116008900} is an apocalyptic number.

8210116008900 is the 2865330-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 8210116008900

8210116008900 is an abundant number, since it is smaller than the sum of its proper divisors (21949876735443).

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

8210116008900 is a wasteful number, since it uses less digits than its factorization.

8210116008900 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 272 (or 133 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 36.

Multiplying 8210116008900 by its sum of digits (36), we get a square (295564176320400 = 17191980²).

8210116008900 divided by its sum of digits (36) gives a square (228058778025 = 477555²).

The spelling of 8210116008900 in words is "eight trillion, two hundred ten billion, one hundred sixteen million, eight thousand, nine hundred".