102 (number)

Basic arithmetic properties

In prime-factor terms, 102 = 2 × 3 × 17. Because it is the product of three distinct primes, 102 is classified as a sphenic number. It is composite and divisible by several smaller integers — the fact of its divisibility is often summarized simply as "102 is divisible by" (divisible).

Divisors

The positive divisors of 102 are listed below; each divisor divides 102 without remainder.

• 1
• 2
• 3
• 6
• 17
• 34
• 51
• 102

Numeric functions and classifications

The sum of all positive divisors (the sigma function) of 102 equals 216, and the sum of its proper divisors (excluding 102 itself) is 114. Because 114 exceeds 102, the number is classified as abundant. Euler's totient function φ(102) equals 32, counting the integers up to 102 that are coprime with it.

Representations and related observations

In binary, 102 is written 1100110; in octal it is 146; in hexadecimal it is 66. The decimal digit sum is 1+0+2 = 3, which reflects its divisibility by 3. Numerically, 102 sits between the prime pair 101 and 103, a simple but neat placement between two successive primes that are themselves twin primes.

History, usage, and notable facts

The written form "one hundred two" (or "one hundred and two" in some varieties of English) and the Roman numeral CII are standard ways to name the number. Outside pure mathematics, the integer 102 appears as the atomic number of the element nobelium and is used as an identifying label in many numbering systems, models, and codes. Its combination of small prime factors and abundant nature makes it a useful example in elementary number theory and teaching.