101122121100 has 1152 divisors, whose sum is σ = 425572761600. Its totient is φ = 17841254400.

The previous prime is 101122121053. The next prime is 101122121131. The reversal of 101122121100 is 1121221101.

It is a Harshad number since it is a multiple of its sum of digits (12).

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 383 ways as a sum of consecutive naturals, for example, 211110661 + ... + 211111139.

It is an arithmetic number, because the mean of its divisors is an integer number (369420800).

Almost surely, 2^101122121100 is an apocalyptic number.

101122121100 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 101122121100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (212786380800).

101122121100 is an abundant number, since it is smaller than the sum of its proper divisors (324450640500).

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

101122121100 is a wasteful number, since it uses less digits than its factorization.

101122121100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 583 (or 576 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 12.

Adding to 101122121100 its reverse (1121221101), we get a palindrome (102243342201).

It can be divided in two parts, 101122 and 121100, that added together give a palindrome (222222).

The spelling of 101122121100 in words is "one hundred one billion, one hundred twenty-two million, one hundred twenty-one thousand, one hundred".