72705635100 has 576 divisors, whose sum is σ = 274532428800. Its totient is φ = 16164126720.

The previous prime is 72705635099. The next prime is 72705635131. The reversal of 72705635100 is 153650727.

72705635100 is a `hidden beast` number, since 7 + 2 + 7 + 0 + 5 + 635 + 10 + 0 = 666.

It is a super-2 number, since 2×72705635100² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

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, 126006012 + ... + 126006588.

It is an arithmetic number, because the mean of its divisors is an integer number (476618800).

Almost surely, 2^72705635100 is an apocalyptic number.

72705635100 is a gapful number since it is divisible by the number (70) 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 72705635100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137266214400).

72705635100 is an abundant number, since it is smaller than the sum of its proper divisors (201826793700).

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

72705635100 is a wasteful number, since it uses less digits than its factorization.

72705635100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 779 (or 766 counting only the distinct ones).

The product of its (nonzero) digits is 44100, while the sum is 36.

The spelling of 72705635100 in words is "seventy-two billion, seven hundred five million, six hundred thirty-five thousand, one hundred".