1. Prime Numbers and Prime Factorization Developed by Kira Shank, M.Ed

2. What you will learn…. How to find prime numbers How to find prime factors using prime factorization

3. Explanation  Prime number – an integer larger than 1 that has only two factors (1 and itself). There are exactly two factors.  1 is not a prime number because it only has 1 factor  Prime Factorization – to find which prime numbers can be multiplied together to make the original number  To find the prime factors of a number, a factor tree can be used.  Break down all factors until they are only prime numbers.

4. Worked Examples Which of these numbers are prime numbers? 4, 11, 32, 61 4 – not prime - factors are 1, 2, 4 11 – prime – factors are 1, 11 32 – not prime – factors are 1, 2, 4, 8, 16, 32 61 – prime – factors are 1, 61

5. Practice Problems Which of these numbers are prime numbers? Explain or show your work. 5, 8, 20, 37

6. Solutions  5: Prime – factors are 1, 5  8: Not Prime – factors are 1, 2, 4, 8  20: Not Prime – factors 1, 2, 4, 5, 10, 20  37: Prime – factors are 1, 37

7. Worked Examples Prime Factorization for a given number can be figured out using a factor tree. What is the prime factorization of 24? Therefore, 2*2*2*3 is the prime factorization 24. 24 64 2223

8. Worked Examples What is the prime factorization of 32? Therefore, 2*2*2*2*2 is the prime factorization for 32. 32 84 2242 22

9. Practice Problems What is the prime factorization of the following numbers?  14  56  100

10. Solutions What is the prime factorization of 14? Therefore, 2*7 is the prime factorization for 14. 14 27

11. Solutions What is the prime factorization of 56? Therefore, 2*2*2*7 is the prime factorization for 56. 56 87 42 22

12. Solutions What is the prime factorization of 100? Therefore, 2*2*5*5 is the prime factorization for 100. 100 10 2525

13. Wrapping Up A prime number is an integer larger than one that has exactly two factors. To find the prime factorization of a number, you must factor the number to all prime numbers. The best way to do this is to use a factor tree.