306 has 12 divisors (see below), whose sum is σ = 702. Its totient is φ = 96.

The previous prime is 293. The next prime is 307. The reversal of 306 is 603.

It can be written as a sum of positive squares in only one way, i.e., 225 + 81 = 15^2 + 9^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a Curzon number.

It is a plaindrome in base 11, base 14 and base 15.

It is a nialpdrome in base 5.

It is a zygodrome in base 5.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (307) by changing a digit.

306 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 5 ways as a sum of consecutive naturals, for example, 10 + ... + 26.

It is a pronic number, being equal to 17×18.

It is a practical number, because each smaller number is the sum of distinct divisors of 306, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (351).

306 is an abundant number, since it is smaller than the sum of its proper divisors (396).

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

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

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

The sum of its prime factors is 25 (or 22 counting only the distinct ones).

The product of its (nonzero) digits is 18, while the sum is 9.

The square root of 306 is about 17.4928556845. The cubic root of 306 is about 6.7386641008.

Adding to 306 its product of nonzero digits (18), we get a square (324 = 18^{2}).

Adding to 306 its reverse (603), we get a palindrome (909).

It can be divided in two parts, 30 and 6, that added together give a triangular number (36 = T_{8}).

The spelling of 306 in words is "three hundred six", and thus it is an aban number and an oban number.

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