2 6 Prime Factorization Warm Up Problem of

2 -6 Prime Factorization Warm Up Problem of the Day Lesson Presentation Course 2

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

Bellwork on slates • • • Write each expression using exponents Example 7 x 7 x 7 = 73 1. 4 x 4 x 4 x 4 2. 3 x 3 x 3 Write each expression as a product of repeated multiplication Example 43 = 4 x 4 x 4 = 64 3. 53 4. 65 5. 114

Bellwork • • • Write each expression using exponents Example 7 x 7 x 7 = 73 1. 4 x 4 x 4 x 4 46 2. 3 x 3 x 3 35 Write each expression as a product of repeated multiplication Example 43 = 4 x 4 x 4 = 64 3. 53 125 4. 65 7776 5. 114 14641

2 -6 Prime Factorization Problem of the Day Nicholas bikes every third day and skates every other day. On April 5 Nicholas biked and skated. When will he do both again? April 11 Course 2

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

2 -6 Prime Insert Factorization Lesson Title Here Vocabulary prime number – a number that has exactly two factors, 1 and itself. composite number – a number that has more than two factors prime factorization – a number written as a product of its prime factors. Course 2

2 -6 Prime Factorization In June 1999, Nayan Hajratwala discovered the first known prime number with more than one million digits. The new prime number, 26, 972, 593 – 1, has 2, 098, 960 digits. 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. 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. Course 2

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

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

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. Course 2

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

2 -6 Prime Factorization Additional Example 2 A: Using a Factor Tree to Find Prime Factorization Write the prime factorization of each number. 24 24 8 · 3 4 · 2 · 3 Write 24 as the product of two factors. Continue factoring until all factors are prime. 2 · 2 · 3 The prime factorization of 24 is 2 · 2 · 3 or 23 · 3. Course 2

2 -6 Prime Factorization Additional Example 2 B: Using a Factor Tree to Find Prime Factorization Write the prime factorization of each number. 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, or 2 · 3 · 5 2. Course 2

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

2 -6 Prime Insert Factorization Lesson Title Here Check It Out: Example 2 B Write the prime factorization of the number. 90 90 45 · 2 9 · 5 · 2 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 · 5 · 2, or 2 · 32 · 5. 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. Course 2

2 -6 Prime Factorization Additional Example 3 A: Using a Step Diagram to Find Prime Factorization Write the prime factorization of each number. 476 2 238 7 119 17 17 1 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 · 7 · 17, or 22 · 7 · 17. Course 2

2 -6 Prime Factorization Additional Example 3 B: Using a Step Diagram to Find Prime Factorization Write the prime factorization of the number. 275 5 55 11 11 1 Divide 275 by 5. Write the quotient below 275. Stop when the quotient is 1. The prime factorization of 275 is 5 · 11, or 52 · 11. Course 2

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

2 -6 Prime Insert Factorization Lesson Title Here Check It Out: Example 3 B Write the prime factorization of the number. 325 5 65 13 13 1 Divide 325 by 5. Write the quotient below 325. Stop when the quotient is 1. The prime factorization of 325 is 5 · 13, or 52 · 13. Course 2

2 -6 Prime Factorization There is only one prime factorization for any given composite number. Example 2 A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result. 2 476 2 238 7 119 17 17 1 7 476 2 68 2 34 17 17 1 The prime factorizations are 2 · 7 · 17 and 7 · 2 · 17, which are the same as 17 · 2 · 7. Course 2

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

2 -6 Prime Insert Factorization Lesson Title Here Lesson Quiz: Part II Write the prime factorization of each number. 4. 27 33 5. 36 22 · 3 2 6. 28 22 · 7 7. 132 22 · 3 · 11 8. 52 22 · 13 22 · 3 3 9. 108 Course 2