102413313313200 has 360 divisors, whose sum is σ = 356128463515968. Its totient is φ = 27254476677120.

The previous prime is 102413313313189. The next prime is 102413313313217. The reversal of 102413313313200 is 2313313314201.

102413313313200 is a `hidden beast` number, since 1 + 0 + 2 + 4 + 1 + 3 + 3 + 1 + 331 + 320 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (360).

It is a super-2 number, since 2×102413313313200² (a number of 29 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 7593476857 + ... + 7593490343.

Almost surely, 2^{102413313313200} is an apocalyptic number.

102413313313200 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 102413313313200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (178064231757984).

102413313313200 is an abundant number, since it is smaller than the sum of its proper divisors (253715150202768).

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

102413313313200 is a wasteful number, since it uses less digits than its factorization.

102413313313200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 17661 (or 17647 counting only the distinct ones).

The product of its (nonzero) digits is 3888, while the sum is 27.

Adding to 102413313313200 its reverse (2313313314201), we get a palindrome (104726626627401).

The spelling of 102413313313200 in words is "one hundred two trillion, four hundred thirteen billion, three hundred thirteen million, three hundred thirteen thousand, two hundred".