125306509133520 has 3840 divisors, whose sum is σ = 563261228974080. Its totient is φ = 25424011468800.

The previous prime is 125306509133401. The next prime is 125306509133527. The reversal of 125306509133520 is 25331905603521.

125306509133520 is a `hidden beast` number, since 1 + 2 + 5 + 3 + 0 + 6 + 5 + 0 + 91 + 33 + 520 = 666.

It is a Cunningham number, because it is equal to 11194039²-1.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (125306509133527) by changing a digit.

It is a polite number, since it can be written in 767 ways as a sum of consecutive naturals, for example, 168649406269 + ... + 168649407011.

It is an arithmetic number, because the mean of its divisors is an integer number (146682611712).

Almost surely, 2^{125306509133520} is an apocalyptic number.

125306509133520 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 125306509133520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (281630614487040).

125306509133520 is an abundant number, since it is smaller than the sum of its proper divisors (437954719840560).

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

125306509133520 is a wasteful number, since it uses less digits than its factorization.

125306509133520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 948 (or 930 counting only the distinct ones).

The product of its (nonzero) digits is 729000, while the sum is 45.

The spelling of 125306509133520 in words is "one hundred twenty-five trillion, three hundred six billion, five hundred nine million, one hundred thirty-three thousand, five hundred twenty".