Overview

710 is a positive integer that follows 709 and precedes 711. As a whole number it appears in arithmetic, calendrical notation and as an identifier in transportation and communications. In Roman numerals it is written DCCX.

Mathematical properties

Arithmetically, 710 is even and composite. Its prime factorization is 2 × 5 × 71. The full set of divisors is 1, 2, 5, 10, 71, 142, 355 and 710, giving eight divisors in total. The sum of all divisors equals 1,296, so the sum of proper divisors (586) is less than 710 and the number is classified as deficient. The Euler totient function φ(710) = 280. In common numeral systems 710 is 1011000110 in binary, 2C6 in hexadecimal and 1306 in octal.

Historical and cultural references

The year AD 710 is notable in East Asian history: in Japan, 710 is commonly cited as the year when the imperial capital moved to Heijō-kyō (present‑day Nara), marking the start of the Nara period in Japanese history. In modern popular culture the sequence 7/10 (July 10) and the number 710 are associated with cannabis concentrates; when turned upside down 710 visually resembles the word "OIL," a link exploited by enthusiasts to celebrate extracts and dabbing on that date.

Uses as an identifier

Numbers such as 710 are frequently used as labels for roads, models and administrative codes. A well‑known example in the United States is Interstate 710, a freeway in the Los Angeles area commonly referred to as the Long Beach Freeway. In numbering plans and technical systems, three‑digit sequences like 710 may be reserved for special services or internal routing rather than for ordinary public assignment.

Notable distinctions and facts

  • 710 is the product of three distinct primes, so it is squarefree (no repeated prime factors).
  • Because the sum of proper divisors is smaller than the number, 710 is a deficient number.
  • Its representation in various bases and the relatively small totient value make it a straightforward example in elementary number theory exercises.

As with most integers, 710 appears across many domains simply as an index, label or date; its mathematical attributes are routine but useful for illustrating factorization, divisor sums and base conversions.