Final answer:
The correct literal to represent the integer value zero is option 1) 0. Other options denote different values and concepts, with null specifically being a non-integer programming construct.
Step-by-step explanation:
To represent the integer value zero, the correct literal is 1) 0. This numeric literal exactly corresponds to the concept of zero in mathematics, meaning no quantity or absence of any count. The other options listed are incorrect as they represent different values: 2) 1 is the integer one, 3) -1 is negative one, and 4) null is a value used in programming to indicate the absence of a value or a non-existent reference, which is not an integer.
In vector algebra, a null vector generalizes the concept of zero, having all components equal to zero and therefore no length and direction. However, this is distinct from the simple integer literal sought here. The basics of factorials and powers of ten are also relevant in determining the place value and significance of zeros in larger numbers, but the literal for the integer value zero is simply '0'