1. Holt CA Course 1 3-1 Prime Factorization Preparation for NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form for a fraction). California Standards

2. Holt CA Course 1 3-1 Prime Factorization VOCABULARY CARDS Prime Number Composite Number Factor Prime Factorization Factor Tree

3. Holt CA Course 1 3-1 Prime Factorization A prime number is a whole number greater than 1 that has exactly two positive factors, 1 and itself. Three is a prime number because its only positive factors are 1 and 3. A composite number is a whole number that has more than two positive factors. Six is a composite number because it has more than two positive factors—1, 2, 3, and 6. The number 1 has exactly one positive factor and is neither prime nor composite.

4. Holt CA Course 1 3-1 Prime Factorization Tell whether each number is prime or composite. Teacher Example 1: Identifying Prime and Composite Numbers 1A. 11 11 is prime. The positive factors of 11 are 1 and 11. 1B. 16 16 is composite. The positive factors of 16 are 1, 2, 4, 8, and 16.

5. Holt CA Course 1 3-1 Prime Factorization Tell whether each number is prime or composite. Student Practice 1: 1A. 14 14 is composite. The positive factors of 14 are 1, 2, 7, and 14. 1B. 7 7 is prime. The positive factors of 7 are 1 and 7.

6. Holt CA Course 1 3-1 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.

7. Holt CA Course 1 3-1 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

8. Holt CA Course 1 3-1 Prime Factorization Write the prime factorization of the number. Teacher Example 2A: Using a Factor Tree to Find Prime Factorization 24 8  3 4  2  3 2  2  2  3 Write 24 as the product of two positive factors. Continue factoring until all factors are prime. The prime factorization of 24 is 2  2  2  3 or 2 3  3.

9. Holt CA Course 1 3-1 Prime Factorization Write the prime factorization of the number. Teacher Example 2B: 150 30  5 10  3  5 2  5  3  5 Write 150 as the product of two positive factors. Continue factoring until all factors are prime. The prime factorization of 150 is 2  3  5  5, or 2  3  5 2.

10. Holt CA Course 1 3-1 Prime Factorization Student Practice 2A: Write the prime factorization of the number. 225 45  5 9  5  5 3  3  5  5 Write 225 as the product of two positive factors. Continue factoring until all factors are prime. The prime factorization of 225 is 3  3  5  5, or 3 2  5 2.

11. Holt CA Course 1 3-1 Prime Factorization Student Practice 2B: Write the prime factorization of the number. 90 45  2 9  5  2 3  3  5  2 Write 90 as the product of two positive factors. Continue factoring until all factors are prime. The prime factorization of 90 is 3  3  5  2, or 2  3 2  5.

12. Holt CA Course 1 3-1 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.

13. Holt CA Course 1 3-1 Prime Factorization Write the prime factorization of the number. Teacher Example 3A: Using a Step Diagram to Find 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.

14. Holt CA Course 1 3-1 Prime Factorization Write the prime factorization of the number. Teacher Example 3B: 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.

15. Holt CA Course 1 3-1 Prime Factorization Student Practice 3A: Write the prime factorization of the 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

16. Holt CA Course 1 3-1 Prime Factorization Student Practice 3B: 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.

17. Holt CA Course 1 3-1 Prime Factorization There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result. 476 238 119 17 1 2 2 7 476 68 34 17 1 7 2 2 The prime factorizations are 2  2  7  17 and 7  2  2  17, which are the same as 17  2  2  7.

18. Holt CA Course 1 3-1 Prime Factorization Lesson Quiz Tell whether each number is prime or composite. 1. 23 2. 393. 27 composite prime composite Write the prime factorization of each number. 4. 27 5. 36 6. 287. 132 8. 529. 108 2 2  3 2 3 2 2  7 2 2  3  11 2 2  13 2 2  3 3