882 (number)

Basic numeric properties

Key arithmetic facts about 882 include:

• Prime factorization: 2 × 3^2 × 7^2
• Number of distinct prime factors (ω): 3; total prime factors with multiplicity (Ω): 5
• Number of positive divisors: 18 (computed as (1+1)(2+1)(2+1) = 18)
• Complete list of positive divisors: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
• Sum of all divisors σ(882) = 2,223; sum of proper divisors = 1,341, so 882 is an abundant number (proper divisor sum > n)
• Euler's totient: φ(882) = 252
• Aliquot sum (sum of proper divisors): 1,341

Representations and patterns

Common numeral and symbolic representations of 882 include decimal 882, binary 1101110010, octal 1562 and hexadecimal 372. In Roman numerals it is written DCCCLXXXII. The sum of its decimal digits is 8+8+2 = 18, so 882 is divisible by 9 and by 3; it is also even, and therefore divisible by 2. Because it is divisible by the sum of its digits, 882 is a Harshad (Niven) number in base 10.

Algebraic and quadratic properties

Because 882 = 2 × 21^2 = 2 × 441 it can be expressed as the sum of two equal squares: 882 = 21^2 + 21^2. More generally, a positive integer that is twice a perfect square has the obvious representation as the sum of two identical squares. The factorization also shows that the primes congruent to 3 modulo 4 (here 3 and 7) occur to even exponents, a condition that permits representation as a sum of two integer squares.

Context and occurrences

As a three‑digit integer, 882 commonly appears in arithmetic exercises, examples of divisibility, and programming or coding challenges. In international telephony the prefix +882 is allocated for global network services and non‑geographic numbers under the ITU E.164 framework, used to route calls for international services rather than to a single country. Beyond mathematics and telecommunications, the sequence "882" is used as an identifier in product model numbers, road signs, and catalogue indexes; such uses are context dependent and carry no inherent mathematical meaning.

Distinguishing facts

Simple classifications: 882 is composite, even, abundant, divisible by 2, 3, 7 and 9, and not a perfect square or a triangular number. Its arithmetic structure (2 times a square) gives it a compact algebraic description and a straightforward geometric interpretation as the sum of two equal squares.