168

168 is an even composite number. Its prime factorization is 2^3 × 3 × 7, and it has 16 divisors in total. The sum of all divisors is 480, so the sum of its proper divisors is 312, making 168 an abundant number.

In various numeral systems, 168 has simple representations: in binary it is 10101000, in octal 250, and in hexadecimal A8. In base 3 it is 20020_3, and in Roman numerals it is CLXVIII.

In mathematics, 168 is notable for its roles in group theory and geometry. It is the order of the simple group PSL(2,7), which is isomorphic to GL(3,2). This group appears as the automorphism group of the Klein quartic and, relatedly, as the full automorphism group of the Fano plane (the projective plane of order 2). The shared order of these symmetry structures highlights 168’s connections between algebra and geometry.

Culturally and practically, 168 is known as the number of hours in a week: seven days multiplied by 24 hours. This common unit is frequently cited in discussions of time management and scheduling, underscoring a daily-life significance beyond abstract mathematics.