813312 has 54 divisors (see below), whose sum is σ = 2351622. Its totient is φ = 270336.

The previous prime is 813311. The next prime is 813343. The reversal of 813312 is 213318.

It can be written as a sum of positive squares in only one way, i.e., 665856 + 147456 = 816^2 + 384^2 .

It is a super-2 number, since 2×813312² = 1322952818688, which contains 22 as substring.

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

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (813311) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 2128 + ... + 2480.

2⁸¹³³¹² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 813312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1175811).

813312 is an abundant number, since it is smaller than the sum of its proper divisors (1538310).

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

813312 is a wasteful number, since it uses less digits than its factorization.

813312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 375 (or 358 counting only the distinct ones).

The product of its digits is 144, while the sum is 18.

The square root of 813312 is about 901.8381229467. The cubic root of 813312 is about 93.3438536894.

The spelling of 813312 in words is "eight hundred thirteen thousand, three hundred twelve".