68

68 is the natural number that follows 67 and precedes 69. It is even and composite, with prime factorization 2^2 × 17. Its divisors are 1, 2, 4, 17, 34, and 68. The sum of all divisors is 126, so the sum of proper divisors is 58, making 68 a deficient number. It is not a prime or a perfect square.

In numeral systems, 68 is written as LXVIII in Roman numerals. In binary it is 1000100; in octal it is 104; and in hexadecimal it is 44.

In science, 68 is the atomic number of erbium, a silvery-white lanthanide metal. Erbium is widely used in fiber-optic technology as a dopant in erbium-doped fiber amplifiers, which help amplify light signals around 1550 nanometers. It is also used in certain solid-state lasers, such as erbium-doped yttrium aluminum garnet (Er:YAG). Beyond optics, erbium finds applications in various high-tech materials and alloys.

Historically, the year 68 CE is notable for the death of Emperor Nero and the subsequent succession crises that led to the Year of the Four Emperors in 69 CE. The year 68 BCE also appears in classical Roman history, while 1968 is a well-known later year with significant global events.