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Holt CA Course 1 3-1 Prime Factorization Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.

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Presentation on theme: "Holt CA Course 1 3-1 Prime Factorization Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview."— Presentation transcript:

1 Holt CA Course Prime Factorization Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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

3 Holt CA Course Prime Factorization Preparation for Number Sense (NS2.4) - Determine the least common multiple and the greatest common divisor of whole numbers; Preparation for Number Sense (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

4 Holt CA Course Prime Factorization Objective: You will learn how to find the prime factorization of composite numbers.

5 Holt CA Course Prime Factorization Vocabulary prime number composite number prime factorization

6 Holt CA Course 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.

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

8 Holt CA Course Prime Factorization Tell whether each number is prime or composite. Check It Out! Example 2 A is composite. The positive factors of 14 are 1, 2, 7, and 14. B. 7 7 is prime. The positive factors of 7 are 1 and 7.

9 Holt CA Course 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. You can also use the “Stairs Method” to find the prime factors of a composite number.

10 Holt CA Course 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

11 Holt CA Course Prime Factorization 24 Write the prime factorization of the number 24. Example 3: Using a Factor Tree to Find Prime Factorization 24 8  3 4  2 2  2 The prime factorization of 24 is 2  2  2  3 or 2 3  3.

12 Holt CA Course Prime Factorization Check It Out! Example 4 90 Write the prime factorization of the number  2 9  5 3  3 The prime factorization of 90 is 3  3  5  2, or 2  3 2  5.

13 Holt CA Course Prime Factorization 150 Write the prime factorization of the number 150. Example 5: Using a Factor Tree to Find Prime Factorization  5 10  3 2  5 The prime factorization of 150 is 2  3  5  5, or 2  3  5 2.

14 Holt CA Course Prime Factorization Check It Out! Example Write the prime factorization of the number  5 9  5 3  3 The prime factorization of 225 is 3  3  5  5, or 3 2  5 2.

15 Holt CA Course Prime Factorization You can also use the “Stairs Method” 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.

16 Holt CA Course Prime Factorization 476 Write the prime factorization of the number 476. Example 7: Using the “Stairs Method” to Find Prime Factorization The prime factorization of 476 is 2  2  7  17, or 2 2  7  17.

17 Holt CA Course 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 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 Prime Factorization 275 Write the prime factorization of the number 275. Example 8: Using the “Stairs Method” to Find Prime Factorization The prime factorization of 275 is 5  5  11, or 5 2  11.

19 Holt CA Course Prime Factorization Check It Out! Example Write the prime factorization of the number The prime factorization of 324 is 2  2  3  3  3  3, or 2 2 

20 Holt CA Course Prime Factorization Check It Out! Example Write the prime factorization of the number The prime factorization of 325 is 5  5  13, or 5 2  13.

21 Holt CA Course Prime Factorization Home Learning On-Line Tutoring Factor Trees Prime Wars Factor Game

22 Holt CA Course Prime Factorization Lesson Quiz Tell whether each number is prime or composite composite prime composite Write the prime factorization of each number    3    3 3


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