101905735680 has 1344 divisors, whose sum is σ = 450465919488. Its totient is φ = 20761804800.

The previous prime is 101905735669. The next prime is 101905735699. The reversal of 101905735680 is 86537509101.

It is a happy number.

101905735680 is a `hidden beast` number, since 1 + 0 + 19 + 0 + 5 + 73 + 568 + 0 = 666.

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 (45).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1008967630 + ... + 1008967730.

Almost surely, 2^101905735680 is an apocalyptic number.

101905735680 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 101905735680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (225232959744).

101905735680 is an abundant number, since it is smaller than the sum of its proper divisors (348560183808).

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

101905735680 is a wasteful number, since it uses less digits than its factorization.

101905735680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 185 (or 158 counting only the distinct ones).

The product of its (nonzero) digits is 226800, while the sum is 45.

The spelling of 101905735680 in words is "one hundred one billion, nine hundred five million, seven hundred thirty-five thousand, six hundred eighty".