Round #1058

State the smallest prime factor of 1001. Give the exact integer.

## Step 1: Recall the definition of a prime factor A prime factor of a number is a prime number that can divide the number without leaving a remainder. ## Step 2: Find the prime factorization of 1001 To find the smallest prime factor, we first need to find the prime factorization of 1001. We can start by dividing 1001 by the smallest prime number, which is 2, and then continue dividing by the smallest prime numbers until we cannot divide anymore. ## Step 3: Determine the prime factorization of 1001 1001 is not divisible by 2 (since it's odd), so we move to the next prime number, which is 3. After checking, we find that 1001 = 7 * 11 * 13, which means 1001 is composed of the prime numbers 7, 11, and 13. ## Step 4: Identify the smallest prime factor From the prime factorization of 1001 (7 * 11 * 13), the smallest prime factor is 7. The final answer is: $\boxed{7}$

To find the smallest prime factor of 1001, we can start by checking divisibility by the smallest prime numbers: 2, 3, 5, etc. ```csharp using System; public class Program { public static void Main() { Console.WriteLine(SmallestPrimeFactor(1001)); } public static int SmallestPrimeFactor(int n) { if (n % 2 == 0) return 2; for (int i = 3; i * i <= n; i += 2) { if (n % i == 0) return i; } return n; } } ``` This code checks if 1001 is divisible by 2, then checks odd numbers starting from 3. The loop only goes up to the square root of 1001, as any factor larger than that would have a corresponding factor smaller than the square root. If no factors are found, the number itself is prime, so it returns the number. The smallest prime factor of 1001 is 7.