1. Warm Up Write each number as a product of two whole numbers in as many ways as possible. 1. 6 2. 16 3. 17 4. 36 1 · 6, 2 · 3 1 · 16, 2 · 8, 4 · 4 1 · 17 Course 2 2-6 Prime Factorization 1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6

2. Learn to find the prime factorizations of composite numbers. Course 2 2-6 Prime Factorization

3. Vocabulary prime number composite number prime factorization Insert Lesson Title Here Course 2 2-6 Prime Factorization

4. Course 2 2-6 Prime Factorization A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. Three is a prime number because its only factors are 1 and 3. The first prime number is 2 The first several prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

5. Course 2 2-6 Prime Factorization A composite number is a whole number that has more than two factors. Six is a composite number because it has more than two factors—1, 2, 3, and 6. The number 1 has exactly one factor and is neither prime nor composite.

6. Tell whether each number is prime or composite. Additional Example 1: Identifying Prime and Composite Numbers Course 2 2-6 Prime Factorization A. 11 11 is prime. The factors of 11 are 1 and 11. B. 16 16 is composite. The factors of 16 are 1, 2, 4, 8, and 16.

7. Tell whether each number is prime or composite. Check It Out: Example 1 Course 2 2-6 Prime Factorization A. 14 14 is composite. The factors of 14 are 1, 2, 7, and 14. B. 7 7 is prime. The factors of 7 are 1 and 7.

8. Course 2 2-6 Prime Factorization A composite number can be written as the product of its prime factors. This is called the prime factorization of the number. You can use a factor tree to find the prime factors of a composite number.

9. Course 2 2-6 Prime Factorization You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor. Writing Math

10. Write the prime factorization of each number. Additional Example 2A: Using a Factor Tree to Find Prime Factorization Course 2 2-6 Prime Factorization 24 8 · 3 4 · 2 2 · 2 Write 24 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 24 is 2 · 2 · 2 · 3 or 2 3 · 3.

11. Write the prime factorization of each number. Additional Example 2B: Using a Factor Tree to Find Prime Factorization Course 2 2-6 Prime Factorization 150 30 · 5 10 · 3 · 5 2 · 5 · 3 · 5 Write 150 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 150 is 2 · 3 · 5 · 5, or 2 · 3 · 5 2.

12. Check It Out: Example 2A Insert Lesson Title Here Course 2 2-6 Prime Factorization Write the prime factorization of each number. 36 18 · 2 9 · 2 · 2 3 · 3 · 2 · 2 Write 36 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 36 is 2 · 2 · 3 · 3 or 2 2 · 3 2.

13. Check It Out: Example 2B Insert Lesson Title Here Course 2 2-6 Prime Factorization Write the prime factorization of the number. 90 45 · 2 9 · 5 · 2 3 · 3 · 5 · 2 Write 90 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 90 is 3 · 3 · 5 · 2, or 2 · 3 2 · 5.

14. Course 2 2-6 Prime Factorization You can also use a step diagram to find the prime factorization of a number. At each step, divide by the smallest possible prime number. Continue dividing until the quotient is 1.

15. Write the prime factorization of each number. Additional Example 3A: Using a Step Diagram to Find Prime Factorization Course 2 2-6 Prime Factorization 476 238 119 17 1 2 2 7 Divide 476 by 2. Write the quotient below 476. Keep dividing by a prime number. Stop when the quotient is 1. The prime factorization of 476 is 2 · 2 · 7 · 17, or 2 2 · 7 · 17.

16. Write the prime factorization of the number. Additional Example 3B: Using a Step Diagram to Find Prime Factorization Course 2 2-6 Prime Factorization 275 55 11 1 5 5 Divide 275 by 5. Write the quotient below 275. Stop when the quotient is 1. The prime factorization of 275 is 5 · 5 · 11, or 5 2 · 11.

17. Check It Out: Example 3A Insert Lesson Title Here Course 2 2-6 Prime Factorization Write the prime factorization of each number. 324 162 81 27 1 2 2 3 3 Divide 324 by 2. Write the quotient below 324. Keep dividing by a prime number. Stop when the quotient is 1. The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or 2 2 · 3 4. 9 3 3 3

18. Check It Out: Example 3B Insert Lesson Title Here Course 2 2-6 Prime Factorization Write the prime factorization of the number. 325 65 13 1 5 5 Divide 325 by 5. Write the quotient below 325. Stop when the quotient is 1. The prime factorization of 325 is 5 · 5 · 13, or 5 2 · 13.

19. Lesson Quiz: Part I Tell whether each number is prime or composite. 1. 23 2. 39 3. 27 composite prime Insert Lesson Title Here composite Course 2 2-6 Prime Factorization

20. Lesson Quiz: Part II Write the prime factorization of each number. 4. 27 5. 36 6. 28 7. 132 8. 52 9. 108 2 2 · 3 2 3 Insert Lesson Title Here 2 2 · 7 2 2 · 3 · 11 Course 2 2-6 Prime Factorization 2 2 · 13 2 2 · 3 3