1×2×3×4

1×2×3×4 is the product of the first four positive integers. Evaluating the expression yields 24. In mathematical notation, this is written as 4!, since the factorial of a positive integer n is defined as the product of all positive integers from 1 to n.

The value 24 counts the number of ways to arrange four distinct objects in a sequence, i.e., the number of permutations of a four-element set. This interpretation highlights the factorial function’s role in counting and combinatorics. Because multiplication is commutative, 1×2×3×4 equals 4×3×2×1, illustrating that the order of factors does not affect the product.

Related concepts include the rising factorial, also written (1)4, which equals 1×2×3×4. In more advanced contexts, the factorial connects to the gamma function via Γ(n+1) = n! for positive integers, providing a continuous extension of the factorial to non-integer values.

Applications of 4! extend to binomial coefficients, where expressions like C(4,k) = 4!/(k!(4−k)!) use factorials in their formulas. The product also appears in series expansions and probability calculations involving permutations, combinations, and other combinatorial structures. Overall, 1×2×3×4 serves as a basic example that links simple multiplication to broader factorial-based concepts in mathematics.