10985313648100 has 243 divisors, whose sum is σ = 27163067859291. Its totient is φ = 3853200489600.

The previous prime is 10985313648047. The next prime is 10985313648173. The reversal of 10985313648100 is 184631358901.

The square root of 10985313648100 is 3314410.

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 150999079396 + 10834314568704 = 388586^2 + 3291552^2 .

It is a super-2 number, since 2×10985313648100² (a number of 27 digits) contains 22 as substring.

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (31) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 10572967381 + ... + 10572968419.

Almost surely, 2^{10985313648100} is an apocalyptic number.

10985313648100 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

10985313648100 is the 3314410-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10985313648100

10985313648100 is an abundant number, since it is smaller than the sum of its proper divisors (16177754211191).

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

10985313648100 is a wasteful number, since it uses less digits than its factorization.

10985313648100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2172 (or 1086 counting only the distinct ones).

The product of its (nonzero) digits is 622080, while the sum is 49.

Multiplying 10985313648100 by its sum of digits (49), we get a square (538280368756900 = 23200870²).

The spelling of 10985313648100 in words is "ten trillion, nine hundred eighty-five billion, three hundred thirteen million, six hundred forty-eight thousand, one hundred".