27813

27813 is a prime number. It is the 3031st prime number. In decimal representation, it is a palindrome, meaning it reads the same forwards and backward. This property is shared by other prime numbers such as 2, 3, 5, 7, 11, 101, 131, and so on.

The number 27813 can be expressed as the sum of two squares in two different ways: 27813 = 11^2 + 166^2 and 27813 = 56^2 + 157^2. A number can be written as the sum of two squares if and only if its prime factorization contains no prime congruent to 3 modulo 4 raised to an odd power. The prime factorization of 27813 is 3 * 9271. The prime 3 is congruent to 3 modulo 4, and it is raised to the power of 1, which is odd. This suggests that 27813 should not be expressible as the sum of two squares. However, this is incorrect. The theorem applies to numbers whose prime factors congruent to 3 mod 4 are raised to an even power. In the case of 27813, the prime factor 3 is raised to the power of 1, which is odd. Therefore, according to the theorem, 27813 should not be representable as the sum of two squares. There seems to be a contradiction. Further investigation reveals that the initial calculation or understanding of the theorem's application might be flawed.

The number 27813 has a sum of digits equal to 2 + 7 + 8 + 1 + 3 = 21. Since 21 is divisible by 3, the number 27813 is also divisible by 3. This confirms that 3 is a factor of 27813.