All Problems
Problem #96 MEDIUM

The Probability That Two Numbers Are Coprime

Paradox Probability Number Theory Math

Problem Statement

Pick two positive integers completely at random from all natural numbers. What is the probability that they share no common factor other than 1 — that is, they are coprime? The answer involves one of the most unexpected appearances of π in all of mathematics. What is it?

Answer & Quick Explanation

Logged-in Users Only

You must be logged in to view the answer and check your solution. Signing up is free and takes less than a minute.

Detailed Editorial Solution

Detailed Editorial Solution is Premium

Unlock detailed step-by-step mathematical proofs, logic explanations, and company-specific interview preparation pathways.