1. An integer with factors 2 and 5

To find an integer that has factors 2 and 5, we can follow these steps: 1. **Understanding Factors**: If an integer has factors 2 and 5, it means that the integer can be expressed as a product of these factors. Specifically, the integer must be a multiple of both 2 and 5. 2. **Finding the Least Common Multiple (LCM)**: The least common multiple of 2 and 5 will give us the smallest integer that has both as factors. The LCM of two numbers is the smallest number that is a multiple of both. 3. **Calculating the LCM**: - The prime factorization of 2 is \(2^1\). - The prime factorization of 5 is \(5^1\). - The LCM is found by taking the highest power of each prime factor: \[ \text{LCM}(2, 5) = 2^1 \times 5^1 = 10 \] 4. **Conclusion**: The smallest integer that has both 2 and 5 as factors is 10. However, any multiple of 10 (like 20, 30, 40, etc.) will also have 2 and 5 as factors. Thus, an integer with factors 2 and 5 is 10, and any integer of the form \(10n\) where \(n\) is an integer will also satisfy this condition.