Fifty‑one is the integer after fifty and before fifty‑two. As an odd number, it is not divisible by 2; its positive integer divisors are 1, 3, 17 and 51. In standard factorization notation 51 = 3 × 17, so it is a composite semiprime (the product of two prime numbers). For a general reference to the numeral and its uses see 51.
Mathematical characteristics
Beyond its factors, 51 has several elementary numeric representations: in binary it is 110011, in hexadecimal it is 0x33, and in Roman numerals it is written LI. Its Euler totient function value is φ(51) = 32, reflecting the count of integers less than 51 that are coprime to it. 51 is not a square or a cube, but it is a centered pentagonal number, appearing in the sequence of centered polygonal figures.
History and context
As with other small integers, 51 has been used since antiquity in counting, measurement and calendrical contexts. It appears in elementary arithmetic examples and in number‑theory exercises illustrating semiprime behavior, divisor sums, and multiplicative functions. Its simple factorization makes it a common example when teaching prime factorization.
Uses and notable associations
The number 51 occurs in several non‑mathematical contexts: it is the atomic number of the chemical element antimony (symbol Sb), and the international telephone country code +51 is assigned to Peru. The phrase "Area 51" refers to a well‑known United States military testing site and has entered popular culture, though that refers to a facility rather than the integer itself.
Quick facts
- Divisors: 1, 3, 17, 51.
- Prime factorization: 3 × 17 (semiprime).
- Binary: 110011; Hex: 33; Roman: LI.
- Euler totient: φ(51) = 32.
- Centered pentagonal number: yes.
Because 51 is small and composite with distinct prime factors, it is frequently used in elementary examples across arithmetic, algebra and introductory number theory. For deeper or external references about the number and its occurrences, see linked resources and specialized texts on integers and elementary number theory.