1×81

1×81 is the product of the integers 1 and 81, yielding 81. In arithmetic, this operation demonstrates the multiplicative identity: multiplying any number by 1 leaves that number unchanged, so 1×81 = 81 and 81×1 = 81.

The number 81 itself has several notable properties. It is a perfect square, since 81 = 9², and it is also a power of 3 (3⁴). This makes it a common example in discussions of squares and powers. In numeral representations, 81 is written as 81 in base-10, LXXXI in Roman numerals, 1010001 in binary, and 51 in hexadecimal.

In a broader mathematical context, 1×81 illustrates the commutative and associative properties of multiplication in the integers: the order of multiplication does not affect the result, and grouping does not change the outcome. The digit sum of 81 is 8+1 = 9, and 81 is divisible by 9 (81/9 = 9), giving it a digital root of 9.

Applications and teaching uses of 1×81 typically emphasize the basic identity property of multiplication and the ease of verifying results through simple checks, such as recognizing that multiplying by 1 returns the original number and relating the product to the underlying structure of 81 as a square and a power of 3.