Prime and composite: up to 100
Numbers can be sorted into two cool teams: Prime and Composite. 🎖️ Prime numbers are special because they only have two factors, while composite numbers have more. Let's become number detectives and learn how to tell them apart!
Concept
Understanding prime and composite numbers is fundamental to number theory and helps with fractions and factoring in the future. **What is a Prime Number?** A prime number is a whole number greater than 1 that has **exactly two factors**: 1 and itself. * **Example: 7** * The only numbers that multiply to make 7 are 1 x 7. * Factors are just {1, 7}. * So, 7 is a prime number. * **Other Prime Numbers:** 2, 3, 5, 11, 13, 17, 19... **What is a Composite Number?** A composite number is a whole number greater than 1 that has **more than two factors**. * **Example: 12** * Factors of 12 are {1, 2, 3, 4, 6, 12}. * Since it has more than two factors, 12 is a composite number. * **Other Composite Numbers:** 4, 6, 8, 9, 10, 14, 15... **The Special Case: The Number 1** The number 1 is **neither prime nor composite**. It only has one factor (itself), so it doesn't fit the definition for either group. **How to Test if a Number is Prime or Composite:** To figure out what a number is, try to find its factors. Let's test the number **15**. 1. Is it divisible by 1? Yes (1 x 15). 2. Is it divisible by 2? No (it's not even). 3. Is it divisible by 3? Yes (3 x 5). 4. Stop! We've already found more than two factors: {1, 3, 5, 15}. Therefore, 15 is a **composite** number. **Visualizing with Arrays:** * **Prime numbers** (like 7) can only be arranged in one long rectangle (1x7). * **Composite numbers** (like 12) can be arranged in multiple ways (1x12, 2x6, 3x4). **Key Idea:** Every whole number greater than 1 is either prime or composite. There are no other options!
Try it
Practice identifying prime and composite numbers! **Identify as Prime or Composite:** 1. 5 2. 9 3. 13 4. 21 5. 31 6. 25 7. 2 8. 18 **True or False:** 9. All even numbers are composite. (Careful!) 10. All odd numbers are prime. 11. The number 1 is a prime number. **Listing Factors to Decide:** 12. List the factors of 16. Is it prime or composite? 13. List the factors of 23. Is it prime or composite? 14. List the factors of 33. Is it prime or composite? **Challenge Problems:** 15. What is the only even prime number? 16. Find two prime numbers that add up to 10. 17. List all the prime numbers between 20 and 30.