48 is the integer that follows forty-seven and precedes forty-nine. It is an even, composite number with several familiar algebraic and practical properties. In ordinary counting it appears in many everyday measures and historical references; for quick reference see 48.

Mathematical characteristics

In arithmetic, 48 factors as 2´ × 3 (that is, 2^4 × 3). It has ten positive divisors and the list of those divisors appears below. The number of positive integers less than and coprime to 48 (its totient) is 16. The sum of its proper divisors is 76, which is greater than 48, so 48 is classified as an abundant number.

  • Positive divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
  • Count of divisors: 10.
  • Binary and hexadecimal: 48 = 110000 (base 2) = 0x30 (base 16).
  • ASCII code 48 represents the character '0' in common encodings.

History, names and cultural notes

The written symbol and concept of 48 arise from the natural number sequence used in counting systems. In cultural and historical contexts, the term "Lower 48" commonly denotes the contiguous United States. In classical music, Johann Sebastian Bach's well-known collection contains 48 preludes and fugues across two books, a fact often cited when discussing musical forms.

Uses and examples

Practical uses of 48 include time spans (48 hours equals two days), packaging (dozens and multiples), and mathematics problems that illustrate divisibility and factorization. In science, the atomic number 48 identifies the element cadmium. In computation and encoding, the numeric value 48 frequently appears because of its role in ASCII and binary representations.

Notable distinctions

48 is a highly composite-friendly number because of its many small prime factors and divisors, making it convenient for division into equal parts. It is an even, composite, and abundant integer that serves as a standard example in elementary number theory and in practical measurement contexts where many equal subdivisions are required. For a brief classification, see even number.