Which statement best describes recursion and its base and recursive cases, as illustrated by the factorial example?

Which statement best describes recursion and its base and recursive cases, as illustrated by the factorial example?

• A. Recursion solves a problem by calling itself with smaller input; base case stops recursion; example: n! = n*(n-1)! with base case 1.
• B. Recursion uses loops only.
• C. Base case is not necessary.
• D. Recursive case does not reduce input.

Answer: (A)

Recursion works by solving a problem by calling itself on a smaller version of that problem, and it relies on a base case to stop. In the factorial example, you express n! as n times (n−1)!, which uses the same idea again on a smaller input. The base case is what ends the chain of self-calls—typically 0! or 1! equals 1—so you eventually return a concrete value instead of continuing indefinitely. The recursive step reduces the input by one each time, guaranteeing progress toward the base case. That combination—self-reference with smaller inputs plus a base case to terminate—is what makes recursion work. The idea that recursion uses loops only, or that a base case isn’t necessary, or that the recursive step doesn’t reduce input, doesn’t fit how recursion actually operates.

Recursion works by solving a problem by calling itself on a smaller version of that problem, and it relies on a base case to stop. In the factorial example, you express n! as n times (n−1)!, which uses the same idea again on a smaller input. The base case is what ends the chain of self-calls—typically 0! or 1! equals 1—so you eventually return a concrete value instead of continuing indefinitely. The recursive step reduces the input by one each time, guaranteeing progress toward the base case. That combination—self-reference with smaller inputs plus a base case to terminate—is what makes recursion work. The idea that recursion uses loops only, or that a base case isn’t necessary, or that the recursive step doesn’t reduce input, doesn’t fit how recursion actually operates.