6768

6768 is a positive integer that follows 6767 and precedes 6769. In mathematics, it is an even, composite number with prime factorization 2^4 × 3^2 × 47. This factorization shows 6768 is divisible by 16, 9, and 47, and it has a total of 30 positive divisors.

The divisors of 6768 can be described as all products 2^a · 3^b · 47^c with a in {0,1,2,3,4}, b in {0,1,2}, and c in {0,1}. Examples of divisors include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 47, 48, 72, 94, 141, 188, 282, 423, 564, 752, 846, 1128, 1692, 2256, 3384, and 6768.

6768 is an abundant number, meaning the sum of its proper divisors exceeds the number itself. The sum of all divisors is sigma(6768) = 19,344, so the sum of proper divisors is 12,576, which is greater than 6,768. Consequently, the ratio sigma(6768)/6768 equals 403/141, about 2.86.

In base representations, 6768 equals 1101001110000 in binary, 0x1A70 in hexadecimal, and 15160 in octal. Its decimal value can be factored as 16 × 9 × 47, highlighting its composite structure and multiple divisibility properties. No widely noted historical events or constants are specifically tied to the number 6768.