101129071680 has 1344 divisors, whose sum is σ = 470771159040. Its totient is φ = 19313344512.

The previous prime is 101129071663. The next prime is 101129071721. The reversal of 101129071680 is 86170921101.

It is a tau number, because it is divible by the number of its divisors (1344).

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 191 ways as a sum of consecutive naturals, for example, 114528519 + ... + 114529401.

It is an arithmetic number, because the mean of its divisors is an integer number (350276160).

Almost surely, 2^101129071680 is an apocalyptic number.

101129071680 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 101129071680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (235385579520).

101129071680 is an abundant number, since it is smaller than the sum of its proper divisors (369642087360).

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

101129071680 is a wasteful number, since it uses less digits than its factorization.

101129071680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 968 (or 955 counting only the distinct ones).

The product of its (nonzero) digits is 6048, while the sum is 36.

Adding to 101129071680 its reverse (86170921101), we get a palindrome (187299992781).

The spelling of 101129071680 in words is "one hundred one billion, one hundred twenty-nine million, seventy-one thousand, six hundred eighty".