101525601600 has 252 divisors, whose sum is σ = 361119010044. Its totient is φ = 27053015040.

The previous prime is 101525601581. The next prime is 101525601607. The reversal of 101525601600 is 6106525101.

It is a happy number.

101525601600 is a `hidden beast` number, since 1 + 0 + 1 + 5 + 2 + 56 + 0 + 1 + 600 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 27153766656 + 74371834944 = 164784^2 + 272712^2 .

It is a super-3 number, since 3×101525601600³ (a number of 34 digits) contains 333 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101525601607) by changing a digit.

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 35 ways as a sum of consecutive naturals, for example, 34803342 + ... + 34806258.

Almost surely, 2^101525601600 is an apocalyptic number.

101525601600 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 101525601600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (180559505022).

101525601600 is an abundant number, since it is smaller than the sum of its proper divisors (259593408444).

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

101525601600 is a wasteful number, since it uses less digits than its factorization.

101525601600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5362 (or 5344 counting only the distinct ones).

The product of its (nonzero) digits is 1800, while the sum is 27.

The spelling of 101525601600 in words is "one hundred one billion, five hundred twenty-five million, six hundred one thousand, six hundred".