102211120100 has 72 divisors (see below), whose sum is σ = 226386838440. Its totient is φ = 40041364480.

The previous prime is 102211120087. The next prime is 102211120129. The reversal of 102211120100 is 1021112201.

It can be written as a sum of positive squares in 12 ways, for example, as 20908581604 + 81302538496 = 144598^2 + 285136^2 .

It is a super-3 number, since 3×102211120100³ (a number of 34 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2998754 + ... + 3032646.

It is an arithmetic number, because the mean of its divisors is an integer number (3144261645).

Almost surely, 2^102211120100 is an apocalyptic number.

102211120100 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 102211120100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (113193419220).

102211120100 is an abundant number, since it is smaller than the sum of its proper divisors (124175718340).

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

102211120100 is a wasteful number, since it uses less digits than its factorization.

102211120100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 34529 (or 34522 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 11.

Adding to 102211120100 its reverse (1021112201), we get a palindrome (103232232301).

The spelling of 102211120100 in words is "one hundred two billion, two hundred eleven million, one hundred twenty thousand, one hundred".