Thirty-four (number)

Mathematical properties

Key arithmetic features of 34 include divisibility by 1, 2, 17 and 34; its proper divisors sum to 20, so it is a deficient number. In multiplicative terms 34 = 2 × 17, which makes it the product of exactly two primes (a semiprime). Its Euler totient is 16, and it appears in the Fibonacci sequence as a Fibonacci number under the standard indexing (F9 = 34 when the sequence begins 1, 1, 2, ...).

• Parity: even — divisible by 2 (see even numbers).
• Factorization: 2 × 17 (semiprime).
• Divisors: 1, 2, 17, 34 (note the link to 1 as a divisor: unit).
• Deficiency: proper divisor sum 20 < 34.

Representation and notation

Common representations of 34 in various bases and notations: decimal 34; binary 100010; octal 42; hexadecimal 22; Roman numeral XXXIV. The sum of its decimal digits is 3 + 4 = 7. As an even composite it satisfies many simple congruences and can be expressed as a sum of two primes in several ways (for example 3 + 31, 5 + 29, 11 + 23), illustrating basic instances of Goldbach-type decompositions.

Beyond pure arithmetic, 34 is the atomic number of the chemical element selenium, a fact often used to link the numeral with chemistry and materials science. Its appearances in calendrical or cultural contexts are varied but generally incidental rather than symbolic.

In summary, thirty-four is a modestly interesting integer: even, semiprime, a Fibonacci term, and readily expressible in multiple positional numeral systems. For additional contexts or numeric references see the provided link placeholder above.