What is represented by an exclamation mark (!) and is calculated by multiplying a whole number by all the whole numbers less than it down to 1?

• A. Factorial
• B. Exponent
• C. Square
• D. Product

Answer: (A)

The term described by the exclamation mark (!) is known as "factorial." The factorial of a whole number ( n ) is calculated by multiplying ( n ) by every whole number less than it down to 1. For example, the factorial of 5, denoted as ( 5! ), is calculated as ( 5 \times 4 \times 3 \times 2 \times 1 = 120 ).

This definition clearly illustrates how the process of calculating a factorial works, emphasizing the concept of multiplication across a sequence of descending whole numbers. Factorials are particularly important in various areas of mathematics, including combinatorics, where they are used in permutations and combinations to calculate the number of different ways to arrange or select items.

The other answers represent different mathematical concepts. An exponent refers to the power to which a number is raised, a square represents a number multiplied by itself, and a product refers to the result of multiplying two or more numbers together. None of these terms align with the specific definition and calculation method provided in the question.