11×81

11×81 denotes the product of the integers 11 and 81. In base-10 arithmetic the product is 891. It can be computed as (10+1)×81 = 810 + 81 = 891, or as 11×80 + 11 = 880 + 11 = 891.

Prime factorization and divisibility: 81 = 3^4, so 11×81 = 3^4 × 11. The result, 891, is divisible by 9 and by 11, since 891 = 9×99 = 11×81. The digit sum of 891 is 8+9+1 = 18, which confirms divisibility by 9, and the alternating sum test confirms divisibility by 11 (8 − 9 + 1 = 0).

Context and properties: 891 is a three-digit integer with factors including 1, 3, 9, 11, 27, 33, 81, 99, 297, and 891. The representation 11×81 also highlights the interaction between the 11-times table and powers of 3 (81 = 3^4). The number is commonly used as a straightforward example in multiplication tables and basic factorization exercises.

Applications: While primarily a numerical example, the product illustrates standard arithmetic rules such as distributivity and the relationship between factorization and divisibility.