13146

13146 is a natural number. It is even and lies between 13145 and 13147. In mathematics, it is notable for having a simple prime factorization and for its use in illustrating basic divisor and representation properties of integers.

Prime factorization and divisors

13146 factors as 2 × 3 × 7 × 313, making it a squarefree number (no prime factor is repeated). Consequently, it has 2^4 = 16 positive divisors. These divisors are 1, 2, 3, 6, 7, 14, 21, 42, 313, 626, 939, 1878, 2191, 4382, 6573, and 13146. The product 42 × 313 equals 13146, reflecting its factorization structure.

Basic arithmetic properties

The sum of the digits of 13146 is 1 + 3 + 1 + 4 + 6 = 15, so the number is divisible by 3 (and by 6, since it is even). It is not divisible by 9, as 15 is not a multiple of 9. The Euler totient function yields φ(13146) = 3744.

Representations

In binary, 13146 is 11001101011010₂. In hexadecimal, it is 0x335A. These representations reflect the same value in different numeral systems and are consistent with its decimal factorization.

Context

As a specific integer with a straightforward factorization, 13146 serves as a concrete example in discussions of divisors, squarefree numbers, and base conversions. It does not correspond to a widely known constant, year, or designation beyond its role as a natural number.