311520 has 96 divisors (see below), whose sum is σ = 1088640. Its totient is φ = 74240.

The previous prime is 311473. The next prime is 311533. The reversal of 311520 is 25113.

It is a tau number, because it is divible by the number of its divisors (96).

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a junction number, because it is equal to n+sod(n) for n = 311496 and 311505.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 311520.

It is an unprimeable number.

311520 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 5251 + ... + 5309.

It is an arithmetic number, because the mean of its divisors is an integer number (11340).

2³¹¹⁵²⁰ is an apocalyptic number.

311520 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 311520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (544320).

311520 is an abundant number, since it is smaller than the sum of its proper divisors (777120).

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

311520 is a wasteful number, since it uses less digits than its factorization.

311520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 80 counting only the distinct ones).

The product of its (nonzero) digits is 30, while the sum is 12.

The square root of 311520 is about 558.1397674418. The cubic root of 311520 is about 67.7894293525.

Adding to 311520 its reverse (25113), we get a palindrome (336633).

It can be divided in two parts, 31 and 1520, that added together give a palindrome (1551).

The spelling of 311520 in words is "three hundred eleven thousand, five hundred twenty".