313616085120 has 480 divisors, whose sum is σ = 1212792924420. Its totient is φ = 77195649024.

The previous prime is 313616085077. The next prime is 313616085157. The reversal of 313616085120 is 21580616313.

313616085120 is a `hidden beast` number, since 3 + 1 + 36 + 1 + 608 + 5 + 12 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 1528497216 + 312087587904 = 39096^2 + 558648^2 .

It is a tau number, because it is divible by the number of its divisors (480).

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 59 ways as a sum of consecutive naturals, for example, 8743062 + ... + 8778858.

Almost surely, 2^313616085120 is an apocalyptic number.

313616085120 is a gapful number since it is divisible by the number (30) 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 313616085120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (606396462210).

313616085120 is an abundant number, since it is smaller than the sum of its proper divisors (899176839300).

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

313616085120 is a wasteful number, since it uses less digits than its factorization.

313616085120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35854 (or 35820 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The spelling of 313616085120 in words is "three hundred thirteen billion, six hundred sixteen million, eighty-five thousand, one hundred twenty".