313513200 has 960 divisors, whose sum is σ = 1549900800. Its totient is φ = 58060800.

The previous prime is 313513169. The next prime is 313513231. The reversal of 313513200 is 2315313.

It is an interprime number because it is at equal distance from previous prime (313513169) and next prime (313513231).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a zygodrome in base 12.

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, 10810786 + ... + 10810814.

It is an arithmetic number, because the mean of its divisors is an integer number (1614480).

Almost surely, 2^313513200 is an apocalyptic number.

313513200 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 313513200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (774950400).

313513200 is an abundant number, since it is smaller than the sum of its proper divisors (1236387600).

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

313513200 is a wasteful number, since it uses less digits than its factorization.

313513200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 87 (or 70 counting only the distinct ones).

The product of its (nonzero) digits is 270, while the sum is 18.

The square root of 313513200 is about 17706.3039621486. The cubic root of 313513200 is about 679.3370124021.

Adding to 313513200 its reverse (2315313), we get a palindrome (315828513).

The spelling of 313513200 in words is "three hundred thirteen million, five hundred thirteen thousand, two hundred".