361296 has 60 divisors (see below), whose sum is σ = 1094548. Its totient is φ = 110592.

The previous prime is 361279. The next prime is 361313. The reversal of 361296 is 692163.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (361279) and next prime (361313).

It can be written as a sum of positive squares in 2 ways, for example, as 69696 + 291600 = 264^2 + 540^2 .

It is a nude number because it is divisible by every one of its digits.

It is an alternating number because its digits alternate between odd and even.

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 361296.

It is an unprimeable number.

361296 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1776 + ... + 1968.

2³⁶¹²⁹⁶ is an apocalyptic number.

361296 is a gapful number since it is divisible by the number (36) 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 361296, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (547274).

361296 is an abundant number, since it is smaller than the sum of its proper divisors (733252).

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

361296 is a wasteful number, since it uses less digits than its factorization.

361296 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 220 (or 211 counting only the distinct ones).

The product of its digits is 1944, while the sum is 27.

The square root of 361296 is about 601.0790297457. The cubic root of 361296 is about 71.2231292950.

It can be divided in two parts, 36 and 1296, that multiplied together give a 6-th power (46656 = 6⁶).

The spelling of 361296 in words is "three hundred sixty-one thousand, two hundred ninety-six".