13536

13536 is a positive integer that lies between 13535 and 13537. In mathematics, it is an even, composite number with several notable factorization properties.

Its prime factorization is 2^5 × 3^2 × 47, which implies it has 36 positive divisors (calculated as (5+1)(2+1)(1+1)). The number is divisible by 32, 16, 8, and 4 due to the 2^5 factor, and it is also divisible by 9 and by 47 because of the 3^2 and 47 factors. A few example divisors include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 94, 141, 188, 282, 423, 564, 846, 1128, 1692, 2256, 3384, 4512, 6768, and 13536.

In base representations, 13536 equals 11010011100000 in binary, 0x34E0 in hexadecimal, and 0o32340 in octal.

Other mathematical properties include that the digit sum is 18, which makes 13536 a Harshad (Niven) number in base 10 since 13536 is divisible by 18 (13536 ÷ 18 = 752). It is not a prime, not a perfect square, and it is not a triangular number; by Fermat’s sum of two squares criterion, it cannot be expressed as a sum of two integer squares because the prime 47 (which is congruent to 3 mod 4) appears with an odd exponent in the factorization.

There are no widely known constants or famous theorems specifically associated with the number 13536. It primarily serves as an example of a structurally rich composite integer with multiple small prime factors.